Question

If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.

Options

• A + B

• A - B

• 2A

• 2B

Answer 1

If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be 2B.

Explanation:-

S_n = An + Bn²

S₁ = A × 1 +B × 1²

= A + B

∵ S₁ = a₁

∴ a₁ = A + B      …(i)

and S₂ = A × 2 + B × 2²

⇒ a₁ + a₂ = 2A + 4B

⇒ (A + B) + a₂ = 2A + 4B        ...[Using (i)]

⇒ a₂ = A + 3B

∴ d = a₂ - a₁ = 2B