If sum of n terms of A.P. is 3n2 + 5n, then its which term is 164 :(A

1.	If sum of n terms of A.P. is 3n2 + 5n, then its which term is 164 :(A) 12th(B) 15th(C) 27th(D) 20th
Answer» Answer is (C) 27^th Given : S_n = 3n² + 5n S₁ = 3(1)² + 5(1) = 8 S₂ = 3(2)² + 5(2) = 22 S₃ = 3(3)² + 5(3) = 42 S₄ = 3(4)² + 5(4) = 68 ∴ a₁ = S₁ = 8 a₂ = S₂ – S₁ ⇒ 22 – 8 ⇒ 14 a₃ = S₂ – S₁ ⇒ 22 – 8 ⇒ 14 a₄ = S₂ – S₁ ⇒ 22 – 8 ⇒ 14 Thus A.P. will be 8, 14, 20, 26 …… 164 a = 8, d = 14 – 8 = 6 and a_n = 164 ∴ 164 = a + (n – 1)d 164 = 8 + (n – 1) (n – 1) = 156/6 = 26 ∴ n = 26 + 1 = 27

If sum of n terms of A.P. is 3n2 + 5n, then its which term is 164 :(A) 12th(B) 15th(C) 27th(D) 20th

Answer»

Answer is (C) 27^th

Given : S_n = 3n² + 5n

S₁ = 3(1)² + 5(1) = 8

S₂ = 3(2)² + 5(2) = 22

S₃ = 3(3)² + 5(3) = 42

S₄ = 3(4)² + 5(4) = 68

∴ a₁ = S₁ = 8

a₂ = S₂ – S₁

⇒ 22 – 8 ⇒ 14

a₃ = S₂ – S₁

⇒ 22 – 8 ⇒ 14

a₄ = S₂ – S₁

⇒ 22 – 8 ⇒ 14

Thus A.P. will be 8, 14, 20, 26 …… 164

a = 8,

d = 14 – 8 = 6 and a_n = 164

∴ 164 = a + (n – 1)d

164 = 8 + (n – 1)

(n – 1) = 156/6 = 26

∴ n = 26 + 1 = 27