+1123 Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?
+1868 \((n-3) + (n-2) + (n-1) + n + (n+1) + (n+2) + (n+ 3) = (28/9)(n + 3) \\ 7n = (28/9)(n + 3)\\ 7n = (28/9)n + 28/3 \\ 63n = 28n + 84 \\ 63n - 28n = 84 \\ 35n = 84\\ n = 84 / 35 = 12 / 5 \\ (n - 3) = (12/5 - 3) = -3 / 5\)
This isn't an integer, but
the answer is \( -3 / 5 \)
Thanks! :)
