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)(4n – 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,...