Question

If the pth, qth and rth terms of a GP are a, b, c, respectively. Prove that aq-r-pcp =1​

Answer 1

Answer:

Answer

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 × 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

Thus, the given result is proved.