if pth term of a gp is p and qth term is q.prove that the nth term is (p (to the power n-q) /q (to the power n-p) ) to the power 1/p-q

Let the first term of the G.P. be a. The common ratio be r.

Then the G.P. will be

a, ar, ar2 .......... arn–1 

 

Given:

pth term (ap) = p

arp-1 = p

 

and qth term (aq) = q

arq-1 = q

 

from (1) and (2), we get

 

Putting the value of r in (1), we get

 

Hence nth term (an) = arn–1

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