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Question

If pth qth and rth term of an A.P. are a,b and c respectively, then a(qr)+b(rp)+c(pq)=?

A
2
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B
1
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C
0
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D
None of these
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Solution

The correct option is C 0
Let A be the first term of the A.P and D be the common difference of the A.P.
Given that
a= pth term
a=A+(p1)D
b = qth term
a=A+(q1)D
c= rth term
a=A+(r1)D
L.H.S =a(qr)+b(rp)+c(pq)=aqar+brbp+cpcq
[(A+(p1)D)(qr)+(A+(q1)D)(rp)+(A+(r1)D)(pq)]
=[A((qr)+(rp)+(pq))+D((p1)(qr)+(q1)(rp)+(r1)(pq))]
=[A×0+D(p(qr)+q(rp)+r(pq)(qr)(rp)(pq))]
=[A×0+D×0]=0

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