Question

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

Answer 1

Let a be the first term and r be the common ratio of the G.P.
According to the given condition,
a₄ = a r³ = x ……………………. (1)
a₁₀ = a r⁹ = y …………………. (2)
a₁₆ = a r¹⁵ = z …………………. (3)
Dividing (2) by (1), we obtain