Question

In an AP, if S_n = n(4n + 1), find the AP.

Answer 1

We know that, the n^th term of an AP is

a_n = S_n – S_{n – 1}

a_n = n(4n + 1) – (n – 1){4(n –1) + 1}   ......[∵ S_n = n (4n + 1)]

⇒ a_n = 4n² + n - (n – 1)(4 n – 3)

= 4n² + n – 4n² + 3n + 4n – 3 = 8n – 3

Put n = 1, a₁ = 8(1) -3 = 5

Put n = 2, a₂ = 8(2) – 3 = 16 – 3 = 13

Put n = 3, a₃ = 8(3) – 3 = 24 – 3 = 21

Hence, the required AP is 5, 13, 21,….