1.
For α,βR\alpha, \beta \in \mathbb{R} and a natural number nn, let

Ar=r1n22+α2r2n2β3r23n(3n1)2A_r = \begin{vmatrix} r & 1 & \dfrac{n^2}{2} + \alpha \\ 2r & 2 & n^2 - \beta \\ 3r-2 & 3 & \dfrac{n(3n-1)}{2} \end{vmatrix}


Then 2A10A52A_{10} - A_5 is: