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Question
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
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Solution
Let a1 and d be the first term and the common difference of the A.P. respectively.
According to the given information
Equating both the values of d obtained in (4) and (5), we obtain
aq - bppqp - q = br - qcqrq - r⇒aq - bppp - q = br - qcrq - r⇒rq - raq - bp = pp - qbr - qc⇒raq - bpq - r = pbr - qcp - q⇒aqr - bprq - r = bpr - cpqp - q
Dividing both sides by pqr, we obtain
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