Question

# If $$x, 2y, 3z$$ are in AP, where the distinct numbers $$x, y, z$$ are in GP, then the common ratio of the GP is:

A
3
B
13
C
2
D
12

Solution

## The correct option is D $$\displaystyle \frac{1}{3}$$Given $$4y = x+3z$$ _____(1)and $$y^{2}=xz$$Let common ratio be $$r$$.$$\therefore \displaystyle \frac{y}{x}= r$$ and $$\displaystyle\frac{z}{x}=r^{2}$$Dividing (1) by x,  $$4\displaystyle\frac{y}{x} = 1+ 3\displaystyle\frac{z}{x}$$$$\Rightarrow 4r=1+3r^{2}$$$$\Rightarrow 3r^{2}-4r+1=0$$$$\Rightarrow (3r-1)(r-1)=0$$$$\Rightarrow r= \displaystyle\frac{1}{3}, 1$$But $$r \neq 1 \quad (\because x,y,z$$ are distinct) $$\therefore r=\displaystyle\frac{1}{3}$$Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More