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

1.	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» 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.

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»

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.