If the sum of first n terms of an A.P. is (3n 2 + 7n), then find its nth term. Hence write its 20 th term.

Question

Philoid · Accepted Answer

S_n = (3n² + 7n)

First term, a = S₁ = [3(1)² + 7(1)]

= [3 + 7] = 5

S₂ = [3(2)² + 7(2)]

a + a + d = [12 + 14]

5 + 5 + d = 13

d = 3

a_n = a + (n – 1)d

= 5 + (n – 1) 3

= 5 + 3n – 3

= 3n + 2

a₂₀ = 3(20) + 2

= 60 + 2 = 62

Hence, it’s 20^th term is 62