Question

The sum of n terms of an AP is 3n² + 5n and then which term of AP is 164.

Answer 1

let the term be m

S = 3n² + 5n

S₁ = a₁ = 3 + 5 = 8

S₂ = a₁ + a₂ = 12 + 10 = 22

⇒ a₂ = S₂ - S₁ = 22 - 8 = 14

S₃ = a₁ + a₂ + a₃ = 27 + 15 = 42

⇒a₃ = S₃ - S₂ = 42 - 22 = 20

∴ Given AP is 8,14,20,.....

Thus a = 8 , d = 6

Given t_m = 164.

164 = [a + (n -1)d]

164 = [(8) + (m -1)6]

164 = [8 + 6m - 6]

164 = [2 + 6m]

162= 6m

m = 162 / 6.

∴ m = 27.