Question

How do you find a set of four consecutive integers whose sum is equal to the sum of the next three consecutive integers immediately following them?

Answer 1

let the 7 numbers be x, x+1, x+2, x+3, x+4, x+5, x+6

$x + x + 1 + x + 2 + x + 3 = x + 4 + x + 5 + x + 6 \\ 4x + 6 = 3x + 15 \\ 4x - 3x = 15 - 6 \\ x = 9$

therefore the numbers are

9, 10, 11, 12, 13, 14, 15.