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In an AP, the ratio of the sum of the first p terms to the sum of the first q terms is p2 : q2. Which one of the following is correct?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. The first term is equal to the common difference
  2. The first term is equal to twice the common difference
  3. The common difference is equal to twice the first term
  4. The first term is equal to square of the common difference

Answer (Detailed Solution Below)

Option 3 : The common difference is equal to twice the first term
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Detailed Solution

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Explanation:

Given:

⇒  = p2/q2

⇒ 

⇒ 2aq +q(p – 1)d = 2ap + p(q – 1)d

⇒ 2a(q – p) = d(q – p) 

⇒ 2a = d or d = 2a

Thus, The common difference is equal to twice of the first term

∴ The Correct answer is Option C

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