The sum of the first n terms of an AP is (5n^2/2 + 3n/2). Find its nth term and the 20th term of this AP

Question

The sum of the first n terms of an AP is \((\frac{5n^2}{2}+\frac{3n}{2}).\) Find its nth term and the 20^th term of this AP

Answer 1

\(S_n=(\frac{5n^2}{2}+\frac{3n}{2})=\frac{1}{2}(5n^2+3n)\)    ........\((i)\)

Replacing n by (n - 1) in (i), we get:

Putting n = 20 in (ii), we get

\(T_{20}=(5\times20)-1=99\)

Hence, the 20^th term is 99.