{"id":27965,"date":"2026-10-18T09:39:59","date_gmt":"2026-10-18T09:39:59","guid":{"rendered":"https:\/\/blog.oratrics.com\/?p=27965"},"modified":"2026-10-18T11:30:10","modified_gmt":"2026-10-18T11:30:10","slug":"consecutive-odd-numbers","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/consecutive-odd-numbers\/","title":{"rendered":"Consecutive Odd Numbers: Definition, Formula, Sum, Solved Examples &amp; Free Worksheet"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"27965\" class=\"elementor elementor-27965\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2d3163e elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"2d3163e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4fdc83e\" data-id=\"4fdc83e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0ba56bf\" data-id=\"0ba56bf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b02e6a1 elementor-widget elementor-widget-heading\" data-id=\"b02e6a1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers: Definition, Formula, Sum, Solved Examples &amp; Free Worksheet\n<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a8a32a0 elementor-widget elementor-widget-text-editor\" data-id=\"a8a32a0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Consecutive odd numbers are odd numbers that come one right after another, always 2 apart. Think of 7, 9, 11, 13. If you have ever been asked to \u201cfind three consecutive odd numbers whose sum is 51,\u201d you have already met them. They turn up in school algebra, number series, and aptitude tests, and the good news is that one simple idea explains almost every question. In this guide, I will walk you through the definition, the formulas, the sum and average, and a set of solved examples. A free worksheet waits at the end.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ec0f286 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"ec0f286\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/demo.oratrics.com\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Book a Free Demo Today<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4dcee4d elementor-widget elementor-widget-image\" data-id=\"4dcee4d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"647\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson-1024x647.png\" class=\"attachment-large size-large wp-image-28100\" alt=\"Consecutive odd numbers explained with a student studying mathematics in a classroom.\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson-1024x647.png 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson-300x190.png 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson-768x486.png 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson-1536x971.png 1536w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Consecutive-Odd-Numbers-Classroom-Lesson.png 1577w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b3ca920\" data-id=\"b3ca920\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d7928ef elementor-widget elementor-widget-html\" data-id=\"d7928ef\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Poppins:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\r\n\r\n<div class=\"toc-wrapper\">\r\n    \r\n    \r\n    <div class=\"custom-toc\" id=\"custom-toc\">\r\n        <div class=\"toc-title\">\r\n            \u2630 Table of Contents\r\n        <\/div>\r\n        <ul class=\"toc-list\" id=\"toc-list\"><\/ul>\r\n    <\/div>\r\n    \r\n<\/div>\r\n\r\n<style>\r\n\/* Parent Fixed Wrapper holding both components together *\/\r\n.toc-wrapper {\r\n    position: fixed;\r\n    top: 150px; \r\n    z-index: 1 !important;\r\n    right: 70px;\r\n    width: 100%;\r\n    max-width: 340px;\r\n    font-family: 'Poppins', sans-serif;\r\n}\r\n\r\n\/* Image Styling *\/\r\n.toc-sticky-image {\r\n    width: 100%;\r\n    height: auto;\r\n    border-radius: 22px; \r\n    margin-bottom: 15px; \r\n    box-shadow: 0 4px 12px rgba(0,0,0,0.05);\r\n    display: block;\r\n}\r\n\r\n\/* TOC Container *\/\r\n.custom-toc {\r\n    background: #fff;\r\n    border: 1px solid #dfe3ea;\r\n    border-radius: 22px;\r\n    padding: 0px 28px;\r\n    width: 100%;\r\n    max-height: 24rem; \r\n    overflow-y: auto;\r\n    box-shadow: 0 2px 8px rgba(0,0,0,0.03);\r\n}\r\n\r\n\/* Title *\/\r\n.custom-toc .toc-title {\r\n    font-size: 25px;\r\n    font-weight: 700;\r\n    color: #17233c;\r\n    position: sticky;\r\n    padding: 0.6rem 0rem;\r\n    background-color: white;\r\n    top: 0px;\r\n    margin-bottom: 12px;\r\n    display: flex;\r\n    align-items: center;\r\n    gap: 10px;\r\n    z-index: 2;\r\n}\r\n\r\n\/* List *\/\r\n.custom-toc .toc-list {\r\n    list-style: none;\r\n    margin: 0;\r\n    padding: 0;\r\n}\r\n\r\n\/* Links *\/\r\n.custom-toc .toc-list li {\r\n    margin-bottom: 22px;\r\n}\r\n\r\n.custom-toc .toc-list a {\r\n    text-decoration: none;\r\n    color: #6b7a99;\r\n    font-size: 14px;\r\n    font-weight: 600;\r\n    transition: 0.3s ease;\r\n    display: inline-block;\r\n}\r\n\r\n\/* Hover Color *\/\r\n.custom-toc .toc-list a:hover {\r\n    color: #8B0000;\r\n}\r\n\r\n\/* H2 Indent *\/\r\n.custom-toc .toc-list .toc-h2 {\r\n    padding-left: 18px;\r\n    font-size: 14px;\r\n}\r\n\r\n\/* Mobile Responsive Adjustments *\/\r\n@media(max-width:768px) {\r\n    .toc-wrapper {\r\n        position: relative;\r\n        top: 0;\r\n        z-index: 1;\r\n        right: 0;\r\n        max-width: 100%;\r\n        margin-bottom: 30px;\r\n    }\r\n\r\n    .custom-toc {\r\n        max-height: none; 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So 1, 3, 5, 7 and 9 are odd. Now pick odd numbers that sit side by side in that list, with none skipped, and you have consecutive odd numbers.<\/span><\/p><p><span style=\"font-weight: 400;\">For example, 15, 17, 19 works. But 15, 19, 23 do not, because 17 and 21 are missing.<\/span><\/p><p><span style=\"font-weight: 400;\">A few things are worth remembering:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The gap between neighbours is always 2.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Every number ends in 1, 3, 5, 7 or 9.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Negative numbers count too, such as -5, -3, -1, 1.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply any set of them and the answer is odd.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Students often confuse these with ordinary consecutive numbers like 4, 5, 6, where the gap is 1. If you keep \u201cgap of 2\u201d in your head, you will avoid most errors.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f07480f\" data-id=\"f07480f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1d1b09f elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"1d1b09f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6685057\" data-id=\"6685057\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-425f848\" data-id=\"425f848\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a506bca elementor-widget elementor-widget-heading\" data-id=\"a506bca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers in Terms of x\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a08117a elementor-widget elementor-widget-text-editor\" data-id=\"a08117a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">In algebra we don\u2019t know the numbers yet, so we give the first one a letter. When you write consecutive odd numbers in terms of x, you let x be an odd number and add 2 each time to get the next one.<\/span><\/p><table><tbody><tr><td><p><b>How many numbers<\/b><\/p><\/td><td><p><b>In terms of x<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">x, x + 2<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">3<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">x, x + 2, x + 4<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">4<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">x, x + 2, x + 4, x + 6<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">5<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">x, x + 2, x + 4, x + 6, x + 8<\/span><\/p><\/td><\/tr><\/tbody><\/table><p><span style=\"font-weight: 400;\">Look closely at the pattern: 2, 4, 6, 8. Not 1, 2, 3, 4. In my classes, this is the slip I see most. Adding 1 gives an even number, and the whole set falls apart.<\/span><\/p><p><span style=\"font-weight: 400;\">You can also build the set around the middle. For three numbers, write x \u2212 2, x, x + 2. This is handy when a question gives you the average or the middle value.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-27a484d\" data-id=\"27a484d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-35ef234 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"35ef234\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b944867\" data-id=\"b944867\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ef805c6\" data-id=\"ef805c6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f9c96c1 elementor-widget elementor-widget-heading\" data-id=\"f9c96c1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers in Terms of n\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b4d8c4f elementor-widget elementor-widget-text-editor\" data-id=\"b4d8c4f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Some books prefer n to x. Here n can be any integer, and the expression 2n + 1 guarantees an odd result every time.<\/span><\/p><table><tbody><tr><td><p><b>How many numbers<\/b><\/p><\/td><td><p><b>In terms of n<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2n + 1, 2n + 3<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">3<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2n + 1, 2n + 3, 2n + 5<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">4<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2n + 1, 2n + 3, 2n + 5, 2n + 7<\/span><\/p><\/td><\/tr><\/tbody><\/table><p><span style=\"font-weight: 400;\">You may also see 2n \u2212 1, 2n + 1, 2n + 3. That is just as correct. Try n = 4 in the first set: 2(4) + 1 = 9, then 11, then 13. Three consecutive odd numbers.<\/span><\/p><p><span style=\"font-weight: 400;\">The only real difference between the two methods is this. With x, you have to say that x is odd. With n, the \u201c2n\u201d part takes care of that for you.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c729156\" data-id=\"c729156\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-02f94c8 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"02f94c8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-6889a21\" data-id=\"6889a21\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a92b41a\" data-id=\"a92b41a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c0935e elementor-widget elementor-widget-heading\" data-id=\"4c0935e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers Formula\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d37c604 elementor-widget elementor-widget-text-editor\" data-id=\"d37c604\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">All the formulas below come from one fact: the numbers form a pattern that grows by 2 each step.<\/span><\/p><ol><li><b> The nth odd number:<\/b><span style=\"font-weight: 400;\"> 2n \u2212 1. The 10th odd number is 2(10) \u2212 1 = 19.<\/span><\/li><li><b> Sum of the first n odd numbers:<\/b><span style=\"font-weight: 400;\"> n\u00b2. Check it: 1 + 3 + 5 + 7 + 9 = 25, and 5\u00b2 = 25.<\/span><\/li><li><b> How many odd numbers lie from a to b:<\/b><span style=\"font-weight: 400;\"> (b \u2212 a) \u00f7 2 + 1.<\/span><\/li><li><b> Sum from a to b:<\/b><span style=\"font-weight: 400;\"> (a + b) \u00f7 2 \u00d7 number of terms.<\/span><\/li><li><b> Sum of k consecutive odd numbers starting at x:<\/b><span style=\"font-weight: 400;\"> kx + k(k \u2212 1).<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">Let\u2019s test formula 5 with three numbers. It gives 3x + 3(2) = 3x + 6, and if you add x + (x + 2) + (x + 4) by hand, you get the same thing.<\/span><\/p><p><span style=\"font-weight: 400;\">Some patterns worth knowing:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Add two consecutive odd numbers and the result is even and divisible by 4. For example, 7 + 9 = 16.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Add three and the result is divisible by 3. For example, 7 + 9 + 11 = 27.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">An even count of them always adds up to an even number, and an odd count adds up to an odd number.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-79a77c7\" data-id=\"79a77c7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4d5bfb2 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"4d5bfb2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-469daf7\" data-id=\"469daf7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e85b0fd\" data-id=\"e85b0fd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6493037 elementor-widget elementor-widget-heading\" data-id=\"6493037\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Sum of Consecutive Odd Numbers\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55952b4 elementor-widget elementor-widget-text-editor\" data-id=\"55952b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">There are two cases here. Either you start from 1, or you don\u2019t.<\/span><\/p><p><b>Starting from 1:<\/b><span style=\"font-weight: 400;\"> just square the count. The first 8 odd numbers add up to 8\u00b2 = 64. Verify: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64.<\/span><\/p><p><b>Starting somewhere else:<\/b><span style=\"font-weight: 400;\"> use the formula for evenly spaced numbers. Suppose you need 21 + 23 + 25 + \u2026 + 49.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Number of terms: (49 \u2212 21) \u00f7 2 + 1 = 15<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Sum: (21 + 49) \u00f7 2 \u00d7 15 = 35 \u00d7 15 = <\/span><b>525<\/b><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ba6b7fd\" data-id=\"ba6b7fd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a168c5a elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"a168c5a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-65f03b0\" data-id=\"65f03b0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b09abe3\" data-id=\"b09abe3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c3c01a1 elementor-widget elementor-widget-heading\" data-id=\"c3c01a1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers List\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7326484 elementor-widget elementor-widget-text-editor\" data-id=\"7326484\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Here are the first twenty, which are good to know by heart:<\/span><\/p><p><span style=\"font-weight: 400;\">1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39<\/span><\/p><p><span style=\"font-weight: 400;\">And a few groups of three to show you can start anywhere:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1, 3, 5<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">11, 13, 15<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">21, 23, 25<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">101, 103, 105<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">The only rule is that the first number must be odd, and you keep adding 2.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9a95c93\" data-id=\"9a95c93\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3125baf elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"3125baf\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f473a03\" data-id=\"f473a03\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-40ee869\" data-id=\"40ee869\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-345075b elementor-widget elementor-widget-heading\" data-id=\"345075b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers 1 to 100\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2468e12 elementor-widget elementor-widget-text-editor\" data-id=\"2468e12\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Between 1 and 100 there are exactly 50 odd numbers. I have split them into rows of ten so they are easy to scan.<\/span><\/p><table><tbody><tr><td><p><b>Row<\/b><\/p><\/td><td><p><b>Numbers<\/b><\/p><\/td><td><p><b>Row sum<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">1<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">1, 3, 5, 7, 9, 11, 13, 15, 17, 19<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">100<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">21, 23, 25, 27, 29, 31, 33, 35, 37, 39<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">300<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">3<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">41, 43, 45, 47, 49, 51, 53, 55, 57, 59<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">500<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">4<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">61, 63, 65, 67, 69, 71, 73, 75, 77, 79<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">700<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">5<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">81, 83, 85, 87, 89, 91, 93, 95, 97, 99<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">900<\/span><\/p><\/td><\/tr><\/tbody><\/table><p><span style=\"font-weight: 400;\">The row sums add up to 2,500. That matches n\u00b2, since 50\u00b2 = 2,500. It is a nice way to see the formula working on real numbers.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0bcca0f\" data-id=\"0bcca0f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5cb7142 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"5cb7142\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-a4c82a1\" data-id=\"a4c82a1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5c624b4\" data-id=\"5c624b4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6b9882d elementor-widget elementor-widget-heading\" data-id=\"6b9882d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Consecutive Odd Numbers Average\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2f78f7a elementor-widget elementor-widget-text-editor\" data-id=\"2f78f7a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Because the numbers are evenly spaced, finding the average is quick.<\/span><\/p><p><b>Average = (first number + last number) \u00f7 2<\/b><\/p><p><span style=\"font-weight: 400;\">There is an even faster trick:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">With an <\/span><b>odd count<\/b><span style=\"font-weight: 400;\"> (3, 5, 7 numbers), the average is the <\/span><b>middle number<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">With an <\/span><b>even count<\/b><span style=\"font-weight: 400;\"> (4, 6 numbers), the average is the <\/span><b>mean of the two middle numbers<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Take 13, 15, 17, 19, 21. The middle number is 17, and (13 + 21) \u00f7 2 is 17 as well.<\/span><\/p><p><span style=\"font-weight: 400;\">For all the odd numbers from 1 to 99, the average is (1 + 99) \u00f7 2 = <\/span><b>50<\/b><span style=\"font-weight: 400;\">. Or divide the total by the count: 2,500 \u00f7 50 = 50.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1995068\" data-id=\"1995068\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-55dfda2 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"55dfda2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-152f1a1\" data-id=\"152f1a1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-db3b572\" data-id=\"db3b572\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6cabe19 elementor-widget elementor-widget-heading\" data-id=\"6cabe19\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Solved Examples\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9e8c698 elementor-widget elementor-widget-text-editor\" data-id=\"9e8c698\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Example 1: Three consecutive odd numbers add up to 51. Find them.<\/b><\/p><p><span style=\"font-weight: 400;\">Let the numbers be x, x + 2, x + 4.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 3x + 6 = 51<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 3x = 45<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x = 15<\/span><\/p><p><span style=\"font-weight: 400;\">The numbers are <\/span><b>15, 17, 19<\/b><span style=\"font-weight: 400;\">. Check: 15 + 17 + 19 = 51.<\/span><\/p><p><b>Example 2: Four consecutive odd numbers add up to 80. Find them.<\/b><\/p><p><span style=\"font-weight: 400;\">Let them be x, x + 2, x + 4, x + 6.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 4x + 12 = 80<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 4x = 68<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x = 17<\/span><\/p><p><span style=\"font-weight: 400;\">The numbers are <\/span><b>17, 19, 21, 23<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 3: The product of two consecutive odd numbers is 143. Find them.<\/b><\/p><p><span style=\"font-weight: 400;\">Let the numbers be x and x + 2.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x(x + 2) = 143<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x\u00b2 + 2x \u2212 143 = 0<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> (x + 13)(x \u2212 11) = 0<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> x = 11 or x = \u221213<\/span><\/p><p><span style=\"font-weight: 400;\">So the pair is <\/span><b>11 and 13<\/b><span style=\"font-weight: 400;\">. The negative pair <\/span><b>\u221213 and \u221211<\/b><span style=\"font-weight: 400;\"> also works, since (\u221213)(\u221211) = 143.<\/span><\/p><p><b>Example 4: Find the sum of the first 15 odd numbers.<\/b><\/p><p><span style=\"font-weight: 400;\">Sum = 15\u00b2 = <\/span><b>225<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 5: Write three consecutive odd numbers in terms of n, then find them if their sum is 45.<\/b><\/p><p><span style=\"font-weight: 400;\">The numbers are 2n + 1, 2n + 3, 2n + 5. Their sum is 6n + 9.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> 6n + 9 = 45, so n = 6.<\/span><\/p><p><span style=\"font-weight: 400;\">The numbers are <\/span><b>13, 15, 17<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>Example 6: The average of five consecutive odd numbers is 41. Find them.<\/b><\/p><p><span style=\"font-weight: 400;\">With five numbers, the average is the middle one. So the middle number is 41, and the set is <\/span><b>37, 39, 41, 43, 45<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-eab5064\" data-id=\"eab5064\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c4d98f3 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"c4d98f3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5a90c14\" data-id=\"5a90c14\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b35b290\" data-id=\"b35b290\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f85ce4d elementor-widget elementor-widget-heading\" data-id=\"f85ce4d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Common Mistakes to Avoid\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c02004c elementor-widget elementor-widget-text-editor\" data-id=\"c02004c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Adding 1 instead of 2.<\/b><span style=\"font-weight: 400;\"> x, x + 1, x + 2 gives consecutive numbers, not consecutive odd numbers.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Starting with an even x.<\/b><span style=\"font-weight: 400;\"> The whole set then turns out even.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Dropping the negative answer.<\/b><span style=\"font-weight: 400;\"> Equations like x(x + 2) = 143 usually have two valid pairs.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Treating \u201cconsecutive\u201d and \u201codd\u201d as separate ideas.<\/b><span style=\"font-weight: 400;\"> Consecutive means no odd number is skipped.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Using n\u00b2 from any starting point.<\/b><span style=\"font-weight: 400;\"> That shortcut only works when you begin at 1.<\/span><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5c34623\" data-id=\"5c34623\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6454cc2 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"6454cc2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1f3a9df\" data-id=\"1f3a9df\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ea7ca7a\" data-id=\"ea7ca7a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c871382 elementor-widget elementor-widget-heading\" data-id=\"c871382\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Free Worksheet: Consecutive Odd Numbers\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8caadc0 elementor-widget elementor-widget-text-editor\" data-id=\"8caadc0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ol><li style=\"font-weight: 400;\" aria-level=\"1\"><p><span style=\"font-weight: 400;\">Give these a go before you look at the answers.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Write the next three consecutive odd numbers after 37.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find three consecutive odd numbers whose sum is 75.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">What is the sum of the first 20 odd numbers?<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find four consecutive odd numbers whose sum is 112.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find the average of five consecutive odd numbers starting from 31.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Find the sum of all odd numbers from 51 to 99.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The product of two consecutive odd numbers is 255. Find them.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The largest of three consecutive odd numbers is 41. Find their sum.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Write three consecutive odd numbers in terms of n, starting with 2n + 1.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">True or false: 9 and 13 are consecutive odd numbers.<\/span><\/li><\/ol><p><b>Answers<\/b><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">39, 41, 43<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">23, 25, 27 (3x + 6 = 75, so x = 23)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">400 (20\u00b2)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">25, 27, 29, 31 (4x + 12 = 112, so x = 25)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">35 (the numbers are 31, 33, 35, 37, 39)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">1,875 (25 terms with an average of 75)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">15 and 17, or \u221217 and \u221215<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">117 (the numbers are 37, 39, 41)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2n + 1, 2n + 3, 2n + 5<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">False, because 11 sits between them<\/span><\/li><\/ol><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-db9cc27\" data-id=\"db9cc27\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-96449a0 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"96449a0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7fef682\" data-id=\"7fef682\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e75967d\" data-id=\"e75967d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-766dda6 elementor-widget elementor-widget-heading\" data-id=\"766dda6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-97f236f elementor-widget elementor-widget-text-editor\" data-id=\"97f236f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Everything about consecutive odd numbers comes back to the gap of 2. Write them as x, x + 2, x + 4 or as 2n + 1, 2n + 3, 2n + 5, use n\u00b2 when you start from 1, and look for the middle number when you need an average. Work through the worksheet a couple of times and these questions will start to feel routine.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ee7aa21\" data-id=\"ee7aa21\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5e3abb3 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"5e3abb3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-d204a65\" data-id=\"d204a65\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1bb2b18\" data-id=\"1bb2b18\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f0099b8 elementor-widget elementor-widget-heading\" data-id=\"f0099b8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f0d2da7 elementor-widget elementor-widget-accordion\" data-id=\"f0d2da7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2521\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2521\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What are consecutive odd numbers?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2521\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2521\"><p><span style=\"font-weight: 400;\">They are odd numbers that follow one another with a difference of 2, like 21, 23, 25.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2522\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2522\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How do I write them in algebra?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2522\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2522\"><p><span style=\"font-weight: 400;\">Use x, x + 2, x + 4 (with x odd), or 2n + 1, 2n + 3, 2n + 5 (with n any integer).<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2523\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2523\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">What is the sum of the first n odd numbers?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2523\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2523\"><p><span style=\"font-weight: 400;\">It is n\u00b2. The first 10 odd numbers add up to 100.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2524\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-2524\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">How many odd numbers are there from 1 to 100?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2524\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-2524\"><p><span style=\"font-weight: 400;\">Fifty.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2525\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-2525\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Is the sum of two consecutive odd numbers odd or even?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2525\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-2525\"><p><span style=\"font-weight: 400;\">Even, and always divisible by 4.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"What are consecutive odd numbers?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">They are odd numbers that follow one another with a difference of 2, like 21, 23, 25.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How do I write them in algebra?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Use x, x + 2, x + 4 (with x odd), or 2n + 1, 2n + 3, 2n + 5 (with n any integer).<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"What is the sum of the first n odd numbers?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">It is n\\u00b2. The first 10 odd numbers add up to 100.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"How many odd numbers are there from 1 to 100?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Fifty.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Is the sum of two consecutive odd numbers odd or even?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Even, and always divisible by 4.<\\\/span><\\\/p>\"}}]}<\/script>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1e6833e\" data-id=\"1e6833e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Consecutive Odd Numbers: Definition, Formula, Sum, Solved Examples &amp; Free Worksheet Consecutive odd numbers are odd numbers that come one [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":28100,"comment_status":"open","ping_status":"open","sticky":false,"template":"rttpg_full_width","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[9],"tags":[],"class_list":["post-27965","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-explorer-program"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Consecutive Odd Numbers: Definition, Formula and Examples<\/title>\n<meta name=\"description\" content=\"What are consecutive odd numbers? 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