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

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