# Consecutive Integers - Definition and Examples

Consecutive integers are integers that differ by 1. For example, the integers 38 and 39 are consecutive integers because they differ by 1.

39 - 38 = 1.

Similarly, -5 and -4 are consecutive integers because they differ also by 1.

-4 - -5 = -4 + 5 = 1.

## More examples of consecutive integers

1. The integers 24, 25, and 26 are consecutive integers

25 - 24 = 1 and 26 - 25 = 1

2. The integers -20, -19, -18 are consecutive integers

-19 - -20 = -19 + 20 = 1

-18 - -19 = -18 + 19 = 1

From what we have seen so far, in order to find consecutive integers, just start with any number and just keep adding 1.

This helps us to generalize the concept of consecutive integers.

Let n be an integer. Then, the first three consecutive integers are n, n + 1, and n + 2

## Consecutive integers word problem

The sum of four consecutive integers is 142. What are the integers?

Let n be the first integer

Then n + 1 is the second integer

n + 2 is the third integer

and n + 3 is the fourth integer

n + n + 1 + n + 2 + n + 3 = 142

4n + 6 = 142

4n = 142 - 6

4n = 136

n = 34

n + 1 = 35

n + 2 = 36

n + 3 = 37

The integers are 34, 35, 36, and 37