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Question

If the pth,qth and rth terms of an A. P. are P, Q, R respectively, then P(q−r)+Q(r−p)+R(p−q) equals ______.

A
0
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B
1
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C
pqr
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D
p + qr
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Solution

The correct option is B 0
Let a be the first term of an A.P and the common difference d.
Tp=a+(p1)d=PTq=a+(q1)d=QTr=a+(r1)d=R
Now,
P(qr)+Q(rp)+R(pq)=PqPr+QrQp+RpRq=q(PR)+r(QP)+p(RQ)=q(pddrd+d)+r(qddpd+d)+p(rddqd+d)=d(qpqr+qrrp+prpq)=0

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