### Sequences And Series Question 19

#### Question 19 - 01 February - Shift 1

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 _______

## Show Answer

#### Answer: 754

#### Solution:

#### Formula: General Term of an AP and Sum of $\mathbf{n}$ terms of an AP

$a_1+a_2+a_3+a_4=50$

$\Rightarrow 32+6 d=50$

$\Rightarrow d=3$

and, $a _{n-3}+a _{n-2}+a _{n-1}+a_n=170$

$\Rightarrow 32+(4 n-10) \cdot 3=170$

$\Rightarrow n=14$

$a_7=26, a_8=29$

$\Rightarrow a_7 \cdot a_8=754$