If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164 ?

Answer: Option B

Sum of n terms of an A.P. = 3n² + 5n
Let a be the first term and d be the common difference
S_n = 3n² + 5n
S₁ = 3(1)² + 5 × 1 = 3 + 5 = 8
S₂ = 3(2)² + 5 × 2 = 12 + 10 = 22
∴ First term (a) = 8
a₂ = S₂ - S₁ = 22 - 8 = 14
d = a₂ - a₁ = 14 - 8 = 6
Now a_n = a + (n - 1)d
⇒ 164 = 8 + (n - 1) × 6
⇒ 6n - 6 = 164 - 8
⇒ 6n = 156 + 6
⇒ 6n = 162
⇒ n = $$\frac{162}{6}$$
⇒ n = 27
∴ 168 is 27^th term