Sum of Five Consecutive Integers Calculator

Calculate the combined sum of five consecutive integers starting from a specified number effortlessly with this calculator.

After understanding the concept of continuous integers, we use N to represent the first integer, then the second to 5th integers can be expressed as: N + 1, N + 2, N + 3 and N + 4.

Therefore, the sum of 5 consecutive integers can be expressed by the formula:

N + (N + 1) + (N + 2) + (N + 3) + (N + 4)

= N + N + 1 + N + 2 + N + 3 + N + 4

= 5 * N + 10

= 5 * (N + 2)

This formula can also be understood as that the sum of 5 consecutive integers is equal to 5 times the third integer.

For example: What is the sum of 5 consecutive integers 15, 16, 17, 18 and 19?

15 + 16 + 17 + 18 + 19 = 85

Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85.

As we all know, even numbers are integers divisible by 2. Therefore, let the first even number is 2 * N, then the remaining 4 consecutive even numbers can be expressed as 2 * N + 2, 2 * N + 4, 2 * N + 6 and 2 * N + 8. Here, N represents an integer.

So, the formula for the sum of 5 consecutive even numbers is

2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8)

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

= 10 * N + 20

= 5 * (2 * N + 4)

That is, the sum of 5 consecutive even numbers is equal to 5 times the third even number.

For example: What is the sum of 5 consecutive even numbers 60, 62, 64, 66 and 68?

60 + 62 + 64 + 66 + 68 = 320

Using the formula to calculate, the third even integer is 64, so its 5 times is 5 * 64 = 320, the answer is correct.

Like 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 remaining 3 consecutive odd numbers can be represented as 2 * N + 3, 2 * N + 5, 2 * N + 7 and 2 * N + 9. N represents an integer.

Therefore, the sum of 5 consecutive odd numbers is

(2 * N + 1) + (2 * N + 3) + (2 * N + 5) + (2 * N + 7) + (2 * N + 9)

= 2 * N + 1 + 2 * N + 3 + 2 * N + 5 + 2 * N + 7 + 2 * N + 9

= 10 * N + 25

= 5 * (2 * N + 5)

Therefore, the sum of 5 consecutive odd numbers is equal to 5 times the third odd number.

For example: What is the sum of 5 consecutive odd numbers 81, 83, 85, 87 and 89?

81 + 83 + 85 + 87 + 89 = 425

Using the formula to calculate, the third odd integer is 85, so its 5 times is 5 * 85= 425. It is consistent with the above answer.

Through the above discussion, you should understand how to calculate the sum of 5 consecutive integers. The sum of 5 consecutive integers is equal to 5 times the third integer. The same is true whether it is consecutive even numbers or consecutive odd numbers.

In addition to manual calculations, this page also provides a calculator for calculating the sum of 5 consecutive integers, so that you can get the sum of 5 consecutive integers faster. The use process is also very simple, input the first integer, then select the integer type. The type can be consecutive integers, consecutive even numbers or consecutive odd numbers. Third, click calculate button to get the answer. No need to think about the whole process. Everyone is welcome to use.