A Neat Sequence

Algebra Level pending

Let \(a_{1}, a_{2}, a_{3}, …, a_{11}\) be real numbers satisfying \(a_{1} = 15, 27 − 2a_{2} > 0\) and \(a_{k} = 2a_{k−1}− a_{k−2}\) for k = 3, 4, …,11.

If \((a_{1}^{2} + a_{2}^{2} +…+a_{11}^{2})/11 = 90\) , then value of \((a_{1} +a_{2} +….+a_{11} )/11\) is ?

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