Seven consecutive integers are added. The sum is 6 times the greatest of the seven integers. what is the smallest integer

the smallest integer is 15

note that consecutive integers have a difference of 1 between them

let the smallest integer be n

then : n, n + 1, n + 2, n + 3, n + 4, n + 5, n + 6

are seven consecutive integers with n + 6 being the largest, thus summing gives

7n + 21 = 6 (6 + n)

7n + 21 = 36 + 6n (distributing right side)

7n - 6n + 21 = 36 (subtracting 6n from both sides)

n + 21 = 36 ⇒ n = 36 - 21 = 15

the smallest integer is 15