# Find Three Consecutive Even Integers Whose Sum is 30 by 3 Ways

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The sum of three consecutive even integers is 30, what the even integers? I can easily tell you that the answer are 8, 10 and 12. You must be interested in how to find these 3 consecutive even integers whose sum is 30. There are three methods here, let us introduce them one by one below.

## 1. Find three consecutive even integers whose sum is 30 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.

Therefore, the sum of 3 consecutive even integers is 30, which can be expressed by the equation

2 * N + (2 * N + 2) + (2 * N + 4) = 30

Solve this equation

2 * N + (2 * N + 2) + (2 * N + 4) = 30

2 * N + 2 * N + 2 + 2 * N + 4 = 30

6 * N + 2 + 4 = 30

6 * N + 6 = 30

6 * N = 30 – 6

6 * N = 24

N = 24 / 6

N = 4

So, 2 * N = 2 * 4 = 8

Now, we can get that 8 is the first integer of 3 consecutive even integers whose sum is 30. So, the second even integer is 10, the third even integer is 12.

The answer came out, the sum of 3 consecutive even integers is 30, these three even integers are 8, 10 and 12.

Verify: 8 + 10 + 12 = 30. Correct!

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

## 2. Find three consecutive even integers whose sum is 30 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 three consecutive even integers whose sum is 30. In here, M = 3, S = 30. Replace them in the formula to calculate the first even integer

First(e) = 30 / 3 – 3 + 1 = 10 – 3 + 1 = 8

The first even integer is 8, so, it can be easily calculated that the second even integer is 10, the third even integer is 12.

Thus, the answer are also 8, 10 and 12. Same as the first method. Then look at the third method, which is the simplest one.

## 3. Find three consecutive even integers whose sum is 30 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 3 consecutive even integers is 30, so, the average of these 3 consecutive even integers is 30 / 3 = 10. The even integers around 10 are 6, 7, 8, 9, 10, 11, 12, 13, 14. Now the problem is simple, find 3 consecutive even integers from 6 to 14 and their average is 10. The answer are 8, 10 and 12.

So the sum of 3 consecutive even integers is 30, these even integers are 8, 10, 12. 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 3 consecutive even integers whose sum is 30, some problems can be easily solved.

• The sum of three consecutive even integers is 30, the smallest one is 8.
• The sum of three consecutive even integers is 30, the middle even integer is 10.
• The sum of three consecutive even integers is 30, the greatest even integer is 12.
• The sum of three consecutive even integers is 30, the average of these even integers is 10.
• The sum of three consecutive even integers is 30, the product of them is 8 * 10 * 12 = 960.
• The sum of three consecutive even integers is 30, the sum of their squares is 82 + 102 + 122 = 308.

## Summarize

On this page, In addition to introducing three methods how to find three consecutive even integers whose sum is 30, it also provides a calculator that calculates three 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 3, 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 three consecutive even integers whose sum is 30. 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?