Question

If the sum of n terms of an AP is $2n^2+3n$, what is the kth term?

Answer 1

Given $S_n=2n^2+3n$

And $S_{n-1}=2(n-1{)}^2+3(n-1)=2(n^2+1-2n)+3n-3=2n^2+2-4n+3n-3=2n^2-n-3$

Then $n^{th}$ term of A.P=$T^n$=$S_n-S_{n-1}=(2n^2+3n)-(2n^2+n-3)=2n^2+3n-2n^2-n+3=2n+3$