Q.

If the pth and qth  terms of a GP are q and p, respectively, then (p-q)th  term is

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a

pqqp1pq

b

qppq1pq

c

qqpp1pq

d

None of these

answer is A.

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Detailed Solution

 let  fist  term be A and common ratio be R. Given, pth term, Tp = q. and q th  term, Tq = p .

ARp1=q and ARq1=p                      ......(i) ARp1ARq1=qp

 Rpq=qpR=qp1pq

On putting  the  value  of -R  in Eq. (i),  we get

Aqpp1pq=qA=qpqp1pq

Now,  (p+g)th  term,Tp+q=ARp+q1

=qpqp1pq×qpp+q1pq=q1p1pq+p+q1pqp+q1pqp1pq=qpqp+1+p+q1pqpp+q1p+1pq=qppqqppq=qppq1pq=qppq1(pq)

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