# Find Six Consecutive Even Integers Whose Sum is 126 by 3 Ways

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The sum of six consecutive even integers is 126, what are these even integers? I can easily tell you that the answer are 16, 18, 20, 22, 24 and 26. You must be interested in how to find these 6 consecutive even integers whose sum is 126. There are three methods here, let us introduce them one by one below.

## 1. Find six consecutive even integers whose sum is 126 by hypothetical method

Assuming that 2 * N is used to represent the first even integer, so the second even integer is 2 * N + 2, the third even integer is 2 * N + 4, the 4th even integer is 2 * N + 6, the 5th even integer is 2 * N + 8, the 6th even integer is 2 * N + 10.

Therefore, the sum of 6 consecutive even integers is 126, which can be expressed by the equation

2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8) + (2 * N + 10) = 126

Solve this equation

2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8) + (2 * N + 10) = 126

2 * N + 2 * N + 2 + 2 * N + 4 + 2 * N + 6 + 2 * N + 8 + 2 * N + 10 = 126

12 * N + 2 + 4 + 6 + 8 + 10 = 126

12 * N + 30 = 126

12 * N = 126 – 30

12 * N = 96

N = 96 / 12

N = 8

So, 2 * N = 2 * 8 = 16

Now, we can get that 16 is the first integer of 6 consecutive even integers whose sum is 126. So, the second even integer is 18, the third even integer is 20, the 4th even integer is 22, the 5th even integer is 24, the 6th even integer is 26.

The answer came out, the sum of 6 consecutive even integers is 126, these three even integers are 16, 18, 20, 22, 24 and 26.

Verify: 16 + 18 + 20 + 22 + 24 + 26 = 126. Correct!

This is the most common method, let’s look at the second method, which is my favorite method.

## 2. Find six consecutive even integers whose sum is 126 by formula method

According to the consecutive integers calculator based on sum, we can know that the sum of M consecutive even integers is S, the first even integer formula is

First(e) = S / M – M + 1

M represents the number of consecutive even integers.

S stands for sum.

Back to the problem we want to solve: find six consecutive even integers whose sum is 126. In here, M = 6, S = 126. Replace them in the formula to calculate the first even integer

First(e) = 126 / 6 – 6 + 1 = 21 – 6 + 1 = 16

The first even integer is 16, so, it can be easily calculated that the second even integer is 18, the third even integer is 20, the 4th even integer is 22, the 5th even integer is 24, the 6th even integer is 26.

Thus, the answer are also 16, 18, 20, 22, 24 and 26. Same as the first method. Then look at the third method, which is the simplest one.

## 3. Find six consecutive even integers whose sum is 126 by average method

The principle is very simple, because we want to calculate the consecutive even integers, so after calculating the average, we can find the even integers near the average.

The sum of 6 consecutive even integers is 126, so, the average of these 6 consecutive even integers is 126 / 6 = 21. The even integers around 21 are 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Now the problem is simple, find 6 consecutive even integers from 13 to 29 and their average is 21. The answer are 16, 18, 20, 22, 24 and 26.

So the sum of 6 consecutive even integers is 126, these even integers are 16, 18, 20, 22, 24, 26. The results are consistent with the above two methods. Is it very simple?

## Problems can be sloved by this answer

Now, we have found out these 6 consecutive even integers whose sum is 126, some problems can be easily solved.

• The sum of six consecutive even integers is 126, the smallest one is 16.
• The sum of six consecutive even integers is 126, the greatest even integer is 26.
• The sum of six consecutive even integers is 126, the average of these even integers is 21.
• The sum of six consecutive even integers is 126, the product of them is 16 * 18 * 20 * 22 * 24 * 26 = 79073280.
• The sum of six consecutive even integers is 126, the sum of their squares is 162 + 182 + 202 + 222 + 242 + 262 = 2716.

## Summarize

On this page, In addition to introducing three methods how to find six consecutive even integers whose sum is 126, it also provides a calculator that calculates six consecutive even integers based on the sum. If you encounter a similar problem next time, you can directly use this calculator to calculate the answer, which is very convenient.

Of course, if the problem you encounter is more complicated, such as: the number of consecutive integers is not 6, or you need to calculate consecutive integers or consecutive odd integers. You can use our other more advanced sum-based consecutive integers calculator, where you can specify the number of consecutive integers and select consecutive integers type: natural integers, odd integers or even integers. I believe it can help you.

Well, that’s it, the above are three solutions to find six consecutive even integers whose sum is 126. Personally, I prefer the second method, because it can accurately calculate the first integer and the calculation process is very simple. So how about you? Please leave a message and tell me which method you like?

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