Q. 145.0( 1 Vote )

# 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 :

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

As n^{th} term of GP is given as –

T_{n} = ar^{n} ^{– 1}

∴ T_{4} = ar^{4 – 1} = ar^{3}

Similarly T_{10} = ar^{9}

And T_{16} = ar^{15}

∴ x = ar^{3}, y = ar^{9} & z = ar^{15}

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

∴ x,y,z are in GP with common ratio r^{6}.Hence proved.

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