If $\displaystyle a_{i}\in\mathbb{R}, i = 1,2,3,...N$and all $\displaystyle a_{i}\ 's$ are distinct such that:

$\displaystyle \left(\sum_{i = 1}^{n - 1} a_{i}^2\right)x^2 + 2\left(\sum_{i = 1}^{n - 1} a_{i}a_{i + 1}\right)x + \sum_{i = 2}^{n} a_{i}^2\leq 0$

,then show that $\displaystyle a_{1},a_{2},a_{3}...$ are in G.P.