Given: 4^th, 10^th and 16^th terms of a G.P. are x, y and z, respectively

Let a be the first term and r be the common ratio of the G.P.

Here,

We know that nth term of the G.P is given by ar^n-1

∴

a₄ = ar³ = x —1

a₁₀ = ar⁹ = y —2

a₁₆ = ar¹⁵ = z —3

Dividing eq-(2) by eq-(1), we obtain

⇒

⇒

Dividing eq(3) by eq-(2), we obtain

⇒

⇒

That is

Thus, x, y, z are in G. P