Question

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

Answer 1

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

According to the given information,

AR^p–1 = a

AR^q–1 = b

AR^r–1 = c

a^q–r b^r–p c^p–q

= A^q–r × R^{(p–1) (q–r)} × A^r-p × R^{(q–1) (r-p)} × A^p–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.