# Warm Problem

Algebra Level 3

Let $$a_1 , a_2, a_3, ... , a_{11}$$ be real numbers satisfying $$a_1 = 15$$ and $$27-a_2 > 0$$ and $$a_k = 2a_{k-1} - a_{k-2}$$ for $$k = 3, 4, ..., 11$$. If $$\frac{a_1^2 + a_2^2+ .... + a_{11}^2}{11} = 90$$ , then the value of $$\frac{a_1+ a_2+...+a_{11}}{11}$$ is equal to

×