Question

Find the rth term of an A.P, the sum of whose first n terms is $3n^2+2n$

Answer 1

Given that, sum of n terms of an AP,
$S_n=2n+3n^2{t}_n=S_n-S_{n-1}=(2n+3n^2)-\left[2\right(n-1)+3(n-1{)}^2]=(2n+3n^2)-[2n-2+3(n^2+1-2n)]=(2n+3n^2)-(2n-2+3n^2+3-6n)=2n+3n^2-2n+2-3n^2-3+6n=6n-1$
$\therefore$ rth term T, = 6r - 1