Question

The sum of $n$ terms of an $A.P.$ is $3n^2+5n$. Find which term of the $A.P.$ is $152$.

Answer 1

$S_1=a_1=3+5=8$

$S_2=a_1+a_2=12+10=22$

$a_2=S_2-S_1=22-8=16$

$S_3=a_1+a_2+a_3=27+15=42$

$a_3=S_3-S_2=42-22=20$

Given $A.P.$

$8,14,\mathrm{20.....}$

$a=8,d=6$

$t_M=152$

$152=[8+(n-1\left)6\right]$

$n=25$

${25}^{th}$ term.