Q. If $a,\ b,\ c$ are in AP, then $3^{a},\ 3^{b},\ 3^{c}$ shall be in
A) AP
B) GP
C) HP
D) None of these
Explanation
(b)
Since, $a,\ b,c$ are in AP.
$\Rightarrow 2b + a + c$
$\therefore\ 3^{2b} = 3^{a + c} \Rightarrow \left( 3^{b} \right)^{2} = 3^{a} \bullet 3^{c}$
$ie,\ 3^{a},\ 3^{b},\ 3^{c}$ are in GP.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.