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Question

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
(a) 0
(b) pq
(c) p + q
(d) − (p + q)


Solution

(d) -p+q

Sp=qp22a+p-1d=q2ap+p-1pd=2q          .....1Sq=pq22a+q-1d=p2aq+q-1qd=2p          .....2Multiplying equation 1 by q and equation 2 by p and then solving, we get:d=-2p+qpqNow, Sp+q=p+q22a+p+q-1d          =p22a+p-1d+qd + q22a+q-1d+pd         =Sp+pqd2+Sq+pqd2         =p+q+pqd          =p+q-2p+qpqpq         =-(p+q)

Mathematics
RD Sharma XI (2015)
Standard XI

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