Fewpal
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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.

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Solution:

Let a be the first term and r be the common ratio of the G.P.

According to the given condition,

a4 = a r3 = x … (1)

a10 = a r9 = y … (2)

a16 = a r15 = z … (3)

Dividing (2) by (1), we obtain

y over x space equals space fraction numerator a r to the power of 9 over denominator a r cubed end fraction space rightwards double arrow y over x space equals space r to the power of 6

Dividing (3) by (2), we obtain

z over y space equals space fraction numerator a r to the power of 15 over denominator a r to the power of 9 end fraction rightwards double arrow z over y equals r to the power of 6

∴  y over x space equals space z over y

Thus, xyz are in G. P.

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