In an A.P if sum of its first n terms is 3n^2 + 5n and its kth term is 164

• Arithmetic Progression (C10)

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

Answer

Here, S_n = 3n² + 5n

⇒ S₁ = 3.1² + 5.1 = 8 = a₁

S₂ = 3.2² + 5.2 = 22 = a₁ + a₂

a₂ = 22 – 8 = 14

⇒ d = 6

t_k = 164

⇒ 8 + (k – 1)6 = 164

⇒ k = 27