Question

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.
• C. 2
• D.

Answer 1

The correct option is B

X,y, and z are in G,P. Hence,

$Y=xr,z=x{r}^2$

Also, x, 2y, and 3z zre in A.P. Hence,

$4y=x+3z$

$\Rightarrow 4xr=x+3x{r}^2$

$\Rightarrow 3r^2-4r+1=0$

$\Rightarrow (3r-1)(r-1)=0$

$\Rightarrow r=1/3(r\ne 1$is not possible as x,y,z are distinct)