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Consecutive Even Numbers: Definition, Formula, Examples & Word Problems

Maybe you’ve got a maths test tomorrow. Maybe a worksheet is due in an hour. Maybe the words “consecutive even numbers” just made your stomach drop a little.

Take a breath. This topic looks scarier than it is.

Here’s the one thing to remember:

Consecutive even numbers go up by 2. So if the first one is x, the next is x + 2, then x + 4, and so on.

That’s it. Really. If you only read this one bit and nothing else, you can already set up most questions on this topic.

If you’ve got a few more minutes, stay. I’ll show you how to use it, and we’ll work through some examples together.

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Consecutive even numbers explained with a student-friendly visual for maths learning.
☰ Table of Contents

    What Are They, Exactly?

    Think of the even numbers as people standing in a queue:

    2, 4, 6, 8, 10, 12, 14…

    “Consecutive” just means standing right next to each other, with nobody skipped. So 8 and 10 are consecutive even numbers. So are 24, 26 and 28. But 8 and 12? No. Poor 10 got left out.

    Even numbers can be negative too, and zero counts as even. So −4, −2, 0, 2 is a perfectly good run of consecutive even numbers. Lots of people forget that.

    The thing that trips almost everyone up

    Why x + 2 and not x + 1?

    Because with normal consecutive numbers like 14, 15, 16, you move up by 1. But with even numbers, you have to hop over the odd ones. So each step is 2.

    Write x + 1 by mistake and you’ll end up with a mix of odd and even numbers. If your answer ever looks weird, check this first. It’s the most common slip by far.

    How to Set Up the Algebra

    Pick the smallest number and call it x. Then keep adding 2.

    How many numbers?

    Write them as

    2

    x, x + 2

    3

    x, x + 2, x + 4

    4

    x, x + 2, x + 4, x + 6

    5

    x, x + 2, x + 4, x + 6, x + 8

    You might see some books write 2n, 2n + 2, 2n + 4 instead. Same thing, different costume. The only difference is that 2n is automatically even, while with x you should check at the end that your answer is even.

    My Five-Step Routine

    I’d give this to any student, whatever the question looks like:

    1. Read it slowly. How many numbers? Even, right?
    2. Call the smallest one x. Add 2 for each next number.
    3. Turn the words into an equation. “Add up to 154” becomes “= 154.”
    4. Solve for x.
    5. Work out the other numbers, then check. Plug them back in. Always.

    Let’s try it.

    Example 1: Two Numbers

    Question: The sum of two consecutive even numbers is 154. What are they?

    Call them x and x + 2.

    x + (x + 2) = 154
     2x + 2 = 154
     2x = 152
     x = 76

    So the numbers are 76 and 78.

    Quick check: 76 + 78 = 154 ✓

    Not bad, right? Two lines of algebra and you’re done.

    Example 2: Three Numbers

    Question: Three consecutive even numbers add up to 138. Find them.

    Call them x, x + 2 and x + 4.

    3x + 6 = 138
     3x = 132
     x = 44

    The numbers are 44, 46 and 48.

    Check: 44 + 46 + 48 = 138 ✓

    Example 3: Four Numbers

    Question: Four consecutive even numbers add up to 308. What are they?

    Call them x, x + 2, x + 4 and x + 6.

    4x + 12 = 308
     4x = 296
     x = 74

    The numbers are 74, 76, 78 and 80.

    Check: 74 + 76 + 78 + 80 = 308 ✓

    Example 4: When the Product Is Given

    This one looks harder, but it’s the same idea with a quadratic on the end.

    Question: The product of two consecutive even numbers is 168. Find them.

    Call them x and x + 2.

    x(x + 2) = 168
     x² + 2x − 168 = 0
     (x + 14)(x − 12) = 0

    So x = 12 or x = −14.

    • If x = 12, the numbers are 12 and 14. (12 × 14 = 168 ✓)
    • If x = −14, the numbers are −14 and −12. (−14 × −12 = 168 ✓)

    Two answers, and both work. Unless the question says “positive numbers,” give both. I’ve watched so many students lose a mark by dropping the negative pair.

    Example 5: Sum of Squares

    Question: The sum of the squares of two consecutive even numbers is 244. Find them.

    Call them x and x + 2.

    x² + (x + 2)² = 244
     2x² + 4x + 4 = 244
     x² + 2x − 120 = 0
     (x + 12)(x − 10) = 0

    So x = 10 or x = −12.

    • 10 and 12: 100 + 144 = 244 ✓
    • −12 and −10: 144 + 100 = 244 ✓

    Word Problems: Same Maths, Different Clothes

    Word problems sound fancy, but they’re hiding the same thing. Your only job is to spot the clue that says “even numbers, one after another.”

    House numbers

    Question: On one side of a street, all the houses have even numbers. Two neighbours’ numbers add up to 410. What are they?

    Neighbours on the same side are 2 apart. Call them x and x + 2.

    2x + 2 = 410
     2x = 408
     x = 204

    The houses are 204 and 206.

    Page numbers

    Question: In a book, left-hand pages have even numbers. Two left-hand pages in a row add up to 90. Which pages are they?

    2x + 2 = 90
     2x = 88
     x = 44

    The pages are 44 and 46.

    Seats in a row

    Question: Five seats in a row have consecutive even numbers, and the numbers add up to 220. What are the seat numbers?

    Call them x, x + 2, x + 4, x + 6 and x + 8.

    5x + 20 = 220
     5x = 200
     x = 40

    The seats are 40, 42, 44, 46 and 48.

    Here’s a little shortcut I like. When there’s an odd number of consecutive numbers, the middle one is just the sum divided by the count. Here, 220 ÷ 5 = 44, and 44 is right in the middle. Step two either way and you’ve got the whole set. No equation needed.

    A Few Patterns Worth Knowing

    These come in handy for checking answers and for “show that…” questions.

    • Two consecutive even numbers: their sum always leaves a remainder of 2 when divided by 4. (76 + 78 = 154, and 154 ÷ 4 leaves 2.)
    • Three consecutive even numbers: their sum is always a multiple of 6. (44 + 46 + 48 = 138 = 6 × 23.)
    • Two consecutive even numbers: their product is always a multiple of 8. (12 × 14 = 168 = 8 × 21.)

    So if a question asks for three consecutive even numbers that add up to 100, you can say straight away it can’t be done. 100 isn’t a multiple of 6. Try the algebra and you’ll see: 3x + 6 = 100 gives x = 31.33. Not even a whole number, never mind an even one.

    And here’s one more, just for fun. If you add the first n even numbers (2 + 4 + 6 + … + 2n), the total is n(n + 1). For the first 10 even numbers, that’s 10 × 11 = 110.

    What About Consecutive Odd Numbers?

    Good news. It’s almost the same.

    Type

    Gap

    Example

    Algebra

    Consecutive numbers

    1

    14, 15, 16

    x, x + 1, x + 2

    Consecutive even numbers

    2

    8, 10, 12

    x, x + 2, x + 4

    Consecutive odd numbers

    2

    7, 9, 11

    x, x + 2, x + 4

    Even and odd use exactly the same algebra. The only difference is whether x starts out even or odd. Learn one and you’ve learned both.

    Mistakes I See All the Time

    Made one of these? Join the club. Everybody has.

    1. Using x + 1 instead of x + 2. That gives you ordinary consecutive numbers.
    2. Stopping once you’ve found x. The question usually wants all the numbers.
    3. Forgetting to check that x is even. If it comes out odd or a fraction, something’s off.
    4. Mixing up the gap and the count. Three numbers means x, x + 2, x + 4. Not x, x + 3, x + 6.
    5. Dropping the negative answer in a quadratic problem.
    6. Skipping the check. It takes ten seconds and it saves marks.

    Now You Try

    Don’t peek at the answers yet. Have a proper go first. It’s the best way to make this stick.

    1. The sum of two consecutive even numbers is 86. Find them.
    2. Three consecutive even numbers add up to 102. Find them.
    3. The product of two consecutive even numbers is 80. Find them.
    4. Four consecutive even numbers add up to 188. Find them.

    Answers:

    1. 42 and 44
    2. 32, 34 and 36
    3. 8 and 10 (or −10 and −8)
    4. 44, 46, 48 and 50

    Got them all? Brilliant. Got one wrong? Check whether you used x + 2 each time. That’s usually where it goes sideways.

    Conclusion

    • Consecutive even numbers go up by 2.
    • Call the smallest one x, then use x + 2, x + 4, x + 6…
    • Make an equation, solve for x, find the rest, and check.
    • Sums give simple equations. Products and sums of squares give quadratics.
    • With an odd count of numbers, the middle one is the sum divided by the count.
    • Odd numbers work exactly the same way.

    If it still feels fiddly, that’s okay. Do the four practice questions above, and I promise it’ll click sooner than you think.

    Frequently Asked Questions

    Even numbers that come one after another, each 2 more than the last. For example, 10, 12 and 14.

    If x is an even number, the next ones are x + 2, x + 4, x + 6 and so on.

    Call them x, x + 2 and x + 4. Write 3x + 6 = the sum, solve for x, then add 2 and 4 to get the other two.

    Yes. It divides exactly by 2. So −2, 0, 2 is a valid set of consecutive even numbers.

    Yes. −8, −6 and −4 are consecutive even numbers.

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