Question

In an $A.P$, if $S_n=n(4n+1)$, find the general form of an A.P.

Answer 1

$S_1=a=5$

$\{a=$ first term, $d=$ common difference$\}$

$S_2=a+(a+d)=2a+d=2\left(9\right)$

$\Rightarrow 10+d=18$

$\Rightarrow d=8$

$\Rightarrow A.P:5,13,21,29,.....$.