Question

The sum of first n terms of an AP is (3n² + 6n). The common difference of the AP is ______.

Options

• 6

• 9

• 15

• –3

Answer 1

The sum of first n terms of an AP is (3n² + 6n). The common difference of the AP is 6.

Explanation:

Given S_n = (3n² + 6n). 

∴ T₁ = S₁

= (3 × 1² + 6 × 1)

= 9

S₂ = (3 × 2² + 6 × 2)

= 24 

∴ T₂ = (S₂ – S₁)

= (24 – 9)

= 15

Hence, d = (T₂ – T₁) 

= 15 – 9

= 6