In an A.P., the sum of first n terms is . Find its 25^th term.

Given, S_n=

_{Let an} be the n^th term of the A.P.

_an= S_n – S_{n – 1}

= 3n²/2 + 13n/2 – 3(n – 1)²/2 – 13(n – 1)/2

= {n² – (n – 1)²} + {n – (n – 1)}

= 3n - +

= 3n + = 3n + 5

Put n = 25

a₂₅= 3(25) + 5

= 75 + 5 = 80

Therefore, 25^th term is a₂₅ = 80