Find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers

Let the four consecutive odd integers be

2n+1, 2n+3, 2n+5, and 2n+7

where n is an integer.

The sum of the smallest and largest integer is

2n+1 + 2n+7 = 4n + 8

The sum of all integers is

2n+1 + 2n+3 + 2n+5 + 2n+7 = 8n + 16

Because the sum of the smallest and largest integer is equal to the sum of all integers,

8n + 16 = 4n + 8

4n = - 8

n = - 2

2n+1 = 2*-2 + 1 = - 3

2n+3 = 2*-2 + 3 = - 1

2n+5 = 2*-2 + 5 = 1

2n+7 = 2*-2 + 7 = 3

Answer:

The four odd integers are - 3, - 1, 1, and 3