Arithmetic Progression (C10)

In an A.P if sum of its first n terms is 3n2 + 5n and its kth term is 164, find the value of k.

Answer

Here, Sn = 3n2 + 5n

⇒ S1 = 3.12 + 5.1 = 8 = a1

S2 = 3.22 + 5.2 = 22 = a1 + a2

a2 = 22 – 8 = 14

⇒ d = 6

tk = 164

⇒ 8 + (k – 1)6 = 164

⇒ k = 27