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  • If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is A. 3 B. 1/3 C. 2 D. 1/2

If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

A. 3

B. 1/3

C. 2

D. 1/2

Answers (1)

It is given that x, 2y and 3z are in A.P

\\ 2y-x=3z-2y \\\\ x=4y-3z \\\\ \frac{y}{x}=\frac{z}{y} \\\\ y^{2}=xz \\\\ y^{2}= \left( 4y-3z \right) z \\\\ y^{2}-4yz+3z^{2}=0 \\\\ \left( 3z-y \right) \left( z-y \right) =0 \\\\ y=3z \ or\ y=z \\\\ r=\frac{y}{z}=\frac{1}{3} \\\\

Hence, correct option is b.

Posted by

infoexpert21

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