Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 14 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
The smallest integer is -17.
(n- 3) +( n -2) + (n - 1) + ( n ) + (n+1) + ( n + 2) + (n + 3) = 14 (n + 3)
7n = 14 (n + 3) divide through by 7
n = 2 ( n + 3)
n = 2n + 6
n -2n = 6
-n = 6
n = -6
The smallest integer is -6 - 3 = -9
