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# If the pth, qth and rth terms of a GP are a,b,c respectively. Prove that aq−rbr−pcp−q=1

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#### Formula,an=arn−1a=arp−1⇒aq−r=(arp−1)q−r........(1)b=arq−1⇒br−p=(brq−1)r−p........(2)c=arr−1⇒cp−q=(crr−1)p−q........(3)multiplying (1),(2) and (3), we get,aq−rbr−pcp−q=(arp−1)q−r(brq−1)r−p(crr−1)p−q=a(p+q+r−p−q−r)r(pq+qr+rp+p+q+r−pq−qr−rp−p−q−r)=a0r0=1Hence proved.

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