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

Asked by Pragya Singh | 1 year ago |  97

##### Solution :-

Let’s take A to be the first term and R to be the common ratio of the G.P.

Then according to the question, we have

ARp–1 = a

ARq–1 = b

ARr–1 = c

Then,

aq–r br–p cp–q

= Aq–r × R(p–1) (q–r) × Ar–p × R(q–1) (r–p) × Ap–q × R(r –1)(p–q)

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

= A0 × R0

= 1

Hence proved.

Answered by Abhisek | 1 year ago

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