# Sum of Three Consecutive Integers Calculator

Sum result:

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The sum of 3 consecutive integers means the addition of three consecutive integers. Compared with the sum of 2 consecutive integers, there is one more addend.

Similarly, before starting, we must understand two concepts: what is an integer and what is continuous. Integers are three types of numbers including negative integers, positive integers, and zero. Continuous integers means that these numbers are all integers, and they are next to each other, there are no other integers between them.

In daily life, in addition to being asked to calculate the sum of 3 consecutive integers, you will also encounter finding the sum of 3 consecutive even integers, or finding the sum of 3 consecutive odd integers. The three situations are discussed separately below.

## Sum of 3 consecutive integers

Through the above discussion, we can know that 3 consecutive integers are adjacent three integers. Therefore, assuming that N is used to represent the first integer, then the second and third integers can be expressed as N+1 and N+2.

So, the sum of 3 consecutive integers can be expressed by the formula

N + (N + 1) + (N + 2)

= N + N + 1 + N + 2

= 3 * N + 3

= 3 * (N + 1)

This formula can be understood as that the sum of 3 consecutive integers is equal to 3 times the second integer.

For example

The sum of 3 consecutive integers starting with 5?

5 is the first integer, so the remaining two integers are 6 and 7. Therefore, the sum between them is 5 + 6 + 7 = 18.

Using the formula to calculate, the second integer is 6, and its triple is 3 * 6 = 18. Consistent with the above results.

## Sum of 3 consecutive even integers

After discussing consecutive integers, let’s move on to consecutive even numbers. Even numbers are integers that are divisible by 2. Obviously, there are two conditions: one is an integer, the other is that it must be divisible by 2. Three consecutive even integers indicate that these three integers must be divisible by 2, and they are next to each other, there are no other even integers between them.

Therefore, assuming that the first even integer is represented by 2 * N, then the second and third even integers are 2 * N + 2 and 2 * N + 4. Here, N represents an integer.

So, the formula for the sum of 3 consecutive even integers is

2 * N + (2 * N + 2) + (2 * N + 4)

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

= 3 * 2 * N + 6

= 3 * (2 * N + 2)

That is, the sum of 3 consecutive even integers is equal to 3 times the second even integer.

E.g

The sum of 3 consecutive even integers 20, 22 and 24.

20 + 22 + 24 = 66

Using the formula to calculate, the second even integer is 22,  and its triple is 3 * 22 = 66, the answer is correct.

## Sum of 3 consecutive odd integers

Similar to even numbers, odd numbers are integers that are not divisible by 2. So, we can use 2 * N + 1 to represent the first integer, then the second and third odd integers are 2 * N + 3 and 2 * N + 5. N represents an integer.

Therefore, the sum of three consecutive odd integers is

(2 * N + 1) + (2 * N + 3) + (2 * N + 5)

= 2 * N +1 + 2 * N + 3 + 2 * N + 5

= 3 * 2 * N + 9

= 3 * (2 * N + 3)

This means that the sum of 3 consecutive odd integers is equal to 3 times the second odd integer.

E.g

The sum of consecutive odd integers 11, 13 and 15.

11 + 13 + 15 = 39

Using the formula to calculate, the second odd integer is 13, and its triple is 3 * 13 = 39. It meets the requirements.

## Conclusion

Through the above discussion, we can come to the same formula, the sum of 3 consecutive integers is equal to three times the second integer. The same is true for the sum of 3 consecutive even integers and the sum of three consecutive odd integers.

Of course, if you don’t want to calculate manually, this page also provides a calculator for the sum of 3 consecutive integers, which can calculate the sum of 3 consecutive integers, the sum of 3 consecutive even integers, and the sum of 3 consecutive odd integers. The use of the calculator is very simple, input the first integer, then select the corresponding integer type, and click Calculate. The answer will be presented immediately. Everyone is welcome to use it!