Question

The sum of $4^{th}$ and $8^{th}$ terms of an AP is $24$ and the sum of $6^{th}$ and ${10}^{th}$ terms is $44$. Find the AP.

Answer 1

given :- sum of $4^{th}$ and $8^{th}$ term is $24$.

$a+3d+a+7d=24$
$2a+10d=24$
$a+5d=\mathrm{12.....}\left(i\right)$

sum of $6^{th}$ and ${10}^{th}$ term is $44$.

$a+5d+a+9d=44$

$12+a+9d=\mathrm{44......}from\left(i\right)$

$a+9d=32$

$a+5d+4d=32$

$12+4d=32$

$d=5$

$a+25=12$

$a=-13$

$AP=-13,-8,-3,2,7,\mathrm{12....}$