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Suppose (m+n)th term of a G.P. is p and (m  n)th term is q, then its nth is

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a
pq
b
pqpm/n
c
pqpm/2n
d
pq

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detailed solution

Correct option is C

Let a be the first term and r be the common ratio.We have           p=am+n=arm+n−1           q=am−n=arm−n−1⇒      pq=am+nam−n=r2n⇒r=pq1/2nNow, an=arn−1=arm+n−1rm=ppq−m/2n=pqpm/2n


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If the first term of an infinite G.P. is 1 and each term is  twice the sum of the succeeding terms, then the common ratio is


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