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If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that aq – r br – pcP – q = 1.

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Let A be the first term and R be the common ratio of the G.P.

According to the given information,

ARp–1 = a

ARq–1 = b

ARr–1 = c

aq–r br–p cp–q

Aq× R(p–1) (q–r) × Arp × R(q–1) (r-p) × Apq × R(–1)(pq)

Aq­ – r + r – p + p – q × R (pr – pr – q + r) + (rq – p – pq) + (pr – p – qr + q)

A0 × R0

= 1

Thus, the given equation is proved.

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