Question

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is ______.

Options

• `1/6`

• `1/5`

• `1/4`

• `1/7`

Answer 1

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is `underlinebb(1/6)`.

Explanation:

Given a = 3 and S₂₅ = S₄₀ – S₂₅

⇒ 2S₂₅ = S₄₀

⇒ `2 xx 25/2[6 + 24d] = 40/2[6 + 39d]`

⇒ 25[6 + 24d] = 20[6 + 39d]

⇒ 5(2 + 8d) = 4(2 + 13d)

⇒ 10 + 40d = 8 + 52d

⇒ d = `1/6`