Question

The sum of n terms of an A.P. is 2n + 3n². Which term of this A.P. is equal to 299?

(a) 11th 

(b) 50th 

(c) 35th 

(d) 29th

Answer 1

Answer: (b) 50th 

S_n = 3n² + 2n 

∴ S_{n –1} = 3(n – 1)² + 2(n – 1) 

= 3n² – 6n + 3 + 2n – 2 = 3n² – 4n + 1 

∴ T_n = S_n – S_{n – 1} = (3n² + 2n) – (3n² – 4n + 1) = 6n – 1. 

Given, T_n = 299 

⇒ 6n – 1 = 299 

⇒ 6n = 300 

⇒ n = 50.