Question

If the sum of first $m$ terms of an $AP$ is $3n^2+5n$ and $m^{th}$ terms is $164$. Find the value of $m$.

Answer 1

Given,

$S_n=3n^2+5n$

$S_1=a=3(1{)}^2+5(1)=8=a_1$

$S_2=a+d=3(2{)}^2+5(2)=22$

$S_2=a_1+a_2$

$a_2=S_2-a_1=22-8=14$

$d=a_2-a_1=14-8=6$

$a_n=a+(n-1)d$

$164=8+(m-1)6$

$164=8+6m-6$

$\therefore m=27$

Hence, this is the answer.