Question

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an A.P. If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

Answer 1

$a_1+a_2+a_3+a_4=50 $
$ \Rightarrow 32+6 d=50 $
$ \Rightarrow d=3 $
$ \text { and, } a_{n-3}+a_{n-2}+a_{n-1}+a_n=170 $
$ \Rightarrow 32+(4 n-10) \cdot 3=170 $
$\Rightarrow n =14 $
$ a_7=26, a_8=29 $
$ \Rightarrow a_7 \cdot a_8=754$