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Question

If pth,qth and rth term of a G.P. are x,y and z respectively prove that :
xarxyrpxzpq=1.

Solution
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Given,

arp1=x

arq1=y

arr1=z

(arp1)qr=xqr

(arq1)rp=yrp

(arr1)pq=zpq

xqryrpzpq=(arp1)qr(arq1)rp(arr1)pq

xqrxyrpxzpq=a(p+q+rpqr)r(pq+qr+rp+p+q+rqprqprpqr)

xqrxyrpxzpq=a0r0

xqrxyrpxzpq=1

Hence proved.

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