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Question

If the terms of a G.P. are a, b and c, respectively. Prove that

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Solution

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

= Aqr × R(p–1) (q–r) × Ar-p × R(q–1) (r-p) × Apq × R(r –1)(pq)

= Aq­r + rp + pq × R (prprq + r) + (rq r + ppq) + (prpqr + q)

= A0 ×R0

= 1

Thus, the given result is proved.


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