Q. If $a,b,c$ are in AP, $b - a,c - b$ and $a$ are in GP, then $a:b:c$ is
A) $1:2:3$
B) $1:3:5$
C) $2:3:4$
D) $1:2:4$
Explanation
(a)
Given $2b = a + c$
and $(c - b)^{2} = (b - a)a$
$\therefore(b - a)^{2} = (b - a)a$
$\Rightarrow \ b = 2a$
$\Rightarrow c = 3a$
$\Rightarrow a:b:c = 1:2:3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.