# 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.

Given: 4th, 10th and 16th 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 arn-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

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