Q. If $a,b$ and $c$ are in AP, then $2^{ax + 1},2^{bx + 1},2^{cx + 1},x \neq 0$ are in
A) AP
B) GP only when $x > 0$
C) GP if $x < 0$
D) GP
Explanation
(d)
Let $b = a + d$ and $c = a + 2d$, where $d$ is common ratio.
Now, $2^{bx + 1} = 2^{(a + d)x + 1} = 2^{ax + 1}.2^{dx}$
and $2^{cx + 1} = 2^{(a + 2d)x + 1} = 2^{ax + 1}.\left( 2^{dx} \right)^{2}$
$\therefore$ These numbers are in GP, for all values of $x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.