Question

If the sum of n term of an AP is ${3n}^2+5n$ then find its $n^{th}$ term.

Answer 1

$S_n=3n^2+5n$

$S_{n-1}=3{(n-1)}^2+5(n-1)$

$=3(n^2-2n+1)+5n-5$

$=3n^2-6n+3+5n-5$

$=3n^2-n-2$

$t_n=S_n-S_{n-1}$

$=3n^2+5n-(3n^2-n-2)$

$=3n^2+5n-3n^2+n+2$

$=6n+2$

$\therefore$ the $n^{th}$ term is $6n+2$