Pearl writes down seven consecutive integers and adds them up. The sum of the integers is equal to 6 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

The answer is 12.

n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6==6(n + 6), solve for n

n == 15 - the smallest integer

Thanks, 15 was correct!