Q. Let the positive numbers $a,\ b,\ c,\ d$ be in AP, then $abc,\ abd,\ acd,\ bcd$ are
A) Not in AP/GP/HP
B) In AP
C) In GP
D) In HP
Explanation
(d)
$a,\ b,\ c,\ d$ are in AP.
$\Rightarrow \frac{a}{abcd},\frac{b}{abcd},\frac{c}{abcd},\frac{d}{abcd}$ are in AP.
$\Rightarrow \ \frac{1}{bcd},\frac{1}{acd},\frac{1}{abd},\frac{1}{abc}$ are in AP.
$\Rightarrow bcd,\ acd,\ abd,\ abc$ are in HP.
$\therefore$ In reverse order $abc,\ abd,\ acd,\ bcd$ are in HP.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.