Question

If the sum of first $8$ and $19$ terms of an A.P. are $64$ and $361$ respectively, find the common difference and sum of its n terms.

Answer 1

$S_8=64$ $\therefore 2a+7d=16$

$S_{19}=361$ $\therefore 2a+18d=38$.

Solving, $a=1,d=2$

$S_n=\left(n/2\right)[2.1+(n-1\left)2\right]=n^2$.