Question

If a, b, c are in A.P., then $10^{ax+10},10^{bx+10},10^{cx+10},x\ne 0are$ 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 $A.P$.
$\therefore 2b=a+c...\left(i\right)$
$\therefore 2bx=\left(a+c\right)x$ for all $x$
Also $2bx+20=\left(a+c\right)x+20$ 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 $x$.