## Word Problems: Consecutive Integer

To solve word problems regarding consecutive integers, it is important to note:

Consecutive Integers: n, n + 1, n + 2, ...

Consecutive Even Integers: n, n + 2, n + 4, ... for even integer n

Consecutive Odd Integers: n, n + 2, n + 4, ... for odd integer n

Example #1:

Solution #1:

Find four consecutive even
integers such that the sum of the second and fourth integers is one and
a half times the sum of the first and third integers.

Solution #1:

Consecutive Even Integers: n, n + 2, n + 4, n + 6 for even integer n

Sum of Second and Fourth Integers: (n + 2) + (n + 6) = 2n + 8

Sum of First and Third Integers: n + (n + 4) = 2n + 4

Since sum of the second and fourth integers is twice than the sum of the first and third integers, it follows that:

2n + 8 = 1.5(2n + 4)

2n + 8 = 3n + 6

3n − 2n = 8 − 6

n = 2

∴ Four consecutive even integers are 2, 4, 6, and 8

Example #2:

Find three consecutive odd
integers such that the sum of the second and third integers is four times the first.

Solution
#2:

Consecutive Even Integers: n, n + 2, n + 4 for odd integer n

Sum of Second and Third Integers: (n + 2) + (n + 4) = 2n + 6

Since sum of the second and third integers equals four times the first integer, it follows that:

2n + 6 = 4n

4n − 2n = 6

2n = 6

n = 3

∴ Three consecutive odd integers are 3, 5 and 7

Related Topics:

- Direct Variation Word Problems
- Inverse Variation Word Problems
- Ideal Gas Law Word Problems
- Age Word Problems