Q. 174.1( 61 Votes )

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

Answer :

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}

∴

a_{4} = ar^{3} = x —1

a_{10} = ar^{9} = y —2

a_{16} = ar^{15} = 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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