Question

The 5^th, 8^th and 11^th terms of a G.P. are p, q and s, respectively. Show that q² = ps.

Answer 1

Let a be the first term and r be the common ratio of the G.P. According to the given condition,
a⁵ = a r^5–1 = a r⁴ = p ………..… (1)
a⁸ = a r^8–1 = a r⁷ = q ………….. (2)
a¹¹ = a r^11–1 = a r¹⁰ = s ………. (3)
Dividing equation (2) by (1), we obtain

Dividing equation (3) by (2), we obtain

Equating the values of r³ obtained in (4) and (5), we obtain

Thus, the given result is proved.