Q4 of 36 Page 161

If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is

The nth term of GP is given by tn = arn-1 where a is the first term and r is the common difference


pth term is given as q


⇒ tp = arp-1


⇒ q = arp-1




qth term is given as p


⇒ tq = arq-1


⇒ p = arq-1




Using (a) and (b)






(p + q)th term is given by


⇒ tp+q = arp+q-1


⇒ tp+q = (arp-1)rq


But tp = arp-1 and the pth term is q


⇒ tp+q = qrq


But









Hence proved the (p + q)th term is .


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