The sum of the first n terms of an AP is . Find its nth term and the 25th term.

Question

Philoid · Accepted Answer

Let a_n be the n^th term of the AP.

To find: a_n and a₂₅

Since, a_n =S_n - S_{n - 1}

= ( ) - ()

= 1/2 (3n² + 5n) - 1/2 [3(n - 1)² + 5(n - 1)]

= 1/2 (3n² + 5n - 3n² - 3 + 6n - 5n + 5)

= 1/2 (6n - 2)

= 3n + 1

Since a_n = 5n - 1

∴ For 25^th term, put n = 25, we get,

a₂₅ = 3(25) + 1

= 75 + 1

= 76