Question

The sum of n terms of an A.P. is 3n². The second term of this A.P. is ______.

Options

• 8

• 3

• 9

• 12

Answer 1

The sum of n terms of an A.P. is 3n². The second term of this A.P. is 9.

Explanation:

Given S_n = 3n²;

S_{n – 1} = 3(n – 1)²

∴ T_n = S_n – S_n–1

= 3n² – 3(n – 1)²

= 3n² – 3[n² – 2n + 1]  ...[∵ (a – b)² = a² – 2ab + b²]

= 3n² – 3n² + 6n – 3

= 6n – 3

∴ T₂ = 6 × 2 – 3

= 12 – 3

= 9