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Formula,

an=arn−1

a=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

=1

Hence proved.

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