Question
Download Solution PDFIn 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
\(\frac{S_p}{S_q} =\frac{p^2}{q^2}\)
⇒ \(\frac{\frac{p}{2}[2a +(p-1)d]}{\frac{q}{2} [2a+(q-1)d]}\) = p2/q2
⇒ \(\frac{2a+(p-1)d}{2a+(q-1)d} =\frac{p}{q}\)
⇒ 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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