Question

$a,b,c$ are in G.P. $a+b+c=bx$ , then $x$ cannot be;

• A. $2$
• B. $-2$
• C. $3$
• D. $4$

Answer 1

The correct option is A

$2$

Explanation for the correct option:

Applying the condition of G.P:

Let the terms of G.P be $\frac{b}{r},b,br$, where $r$ is common ratio

$\because$$a+b+c=bx$

Put the values of $1st,2nd,$and $3rd$ term of GP

$\Rightarrow$$\frac{b}{r}+b+br=bx$

$\Rightarrow$ $x=\frac{1}{r}+1+r$

$\Rightarrow$ $x-1=r+\frac{1}{r}$

But $r+\frac{1}{r}\ge 2$ or $r+\frac{1}{r}\le -2$ $[\because A.M\ge G.M]$

$\Rightarrow$ $x-1\ge 2$ or $x-1\le -2$

$\Rightarrow$ $x\ge 3$ or $x\le -1$

$\therefore$$x$ cannot be $2$

Hence, option ‘A’ is correct.