The sum of the first n terms of an AP is . Find the nth term and the 20th term of this AP.

Question

Philoid · Accepted Answer

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

To find: a_n and a₂₀

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

= ( ) - ()

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

= 1/2 (5n² + 3n - 5n² - 5 + 10n - 3n + 3)

= 1/2 (10n - 2)

= 5n - 1

Since a_n = 5n - 1

∴ For 20^th term, put n = 20, we get,

a₂₀ = 5(20) - 1

= 100 - 1

= 99