Q. 145.0( 1 Vote )

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

Answer :

Let first term of GP be a and common ratio be r

As nth term of GP is given as –

Tn = arn – 1

T4 = ar4 – 1 = ar3

Similarly T10 = ar9

And T16 = ar15

x = ar3, y = ar9 & z = ar15

Clearly we observed that x, y, z have a common ratio.

x,y,z are in GP with common ratio r6.Hence proved.

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