Question

If the sum of first 8 and 19 terms of an A.P. are 64 and 361 respectively, Let the common difference be $d$.Find $d$ .

Answer 1

$S_8=64$

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

$2a+7d=16$
$S_{19}=361$
$2a+18d=38$
Solving, $a=1,d=2$