Q14 of 176 Page 20

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.

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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