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. $\frac{1}{3}$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{1}{3}$

Answer 2

Since, $x, 2y$ and $3z$ are in $A.P$. $\therefore 4y = x + 3z \quad ...(i)$ and $x,y,z$ are in $G.P$. $\therefore y-rx$ and $z = xr^2$ On putting the values of $y$ and $z$ in $(i)$, we get $4xr = x + 3xr^2$ $\Rightarrow 3r^2 - 4r + 1 = 0$ $\Rightarrow (3r - 1)( r - 1 ) = 0$ $\Rightarrow r= \frac{1}{3}, 1$ $\therefore r= \frac{1}{3} \quad\left(\because r\ne1\right)$