Question

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

Answer 1

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