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

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