Question

If a, b, c are in A.P., then $10^{ax + 10}, 10^{bx + 10}, 10^{cx+10},x \neq 0 \, are$ are in

• A. A.P
• B. G.P. only when x > 0
• C. G.P. for all x
• D. G.P. only when x < 0.

Answer 1

Answer: (C)

Since $a, b, c$ are in $A.P$.
$\therefore 2b=a+c\quad...\left(i\right)$
$ \therefore 2bx = \left(a+c\right)x$ for all $x$
Also $2\,bx +20 = \left(a+c\right)x + 20$ for all $x $
$ 10^{2\left(bx+10\right)} = 10^{\left(ax+10\right)+\left(cx+10\right)}$
$\Rightarrow \left(10^{bx+10}\right)^{2} = 10^{ax+10} 10^{cx+10} $
$ \Rightarrow 10^{ax+10} , 10^{bx+10}, 10^{cx+10}$ are in $G.P$. for all $x$.