If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms i

1.	If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164? A. 26th B. 27th C. 28th D. none of these
Answer» Here, S_n = 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.

If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164? A. 26th B. 27th C. 28th D. none of these

Answer»

Here, S_n = 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.