Q. If three real numbers $a,b,c$ are in harmonic progression, then which of the following is true?
A) $\frac{1}{a},b,\frac{1}{c}$ are in AP
B) $\frac{1}{bc},\frac{1}{ca},\frac{1}{ab}$ are in HP
C) $ab,bc,ca$ are in HP
D) $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in HP
Explanation
(b)
Since, $a,b,c$ are in HP.
$\therefore\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in AP.
$\Rightarrow \frac{abc}{a},\frac{abc}{b},\frac{abc}{c}$ are in AP
$\Rightarrow bc,\ ca,\ ab$ are in AP
$\Rightarrow \frac{1}{bc},\frac{1}{ca},\frac{1}{ab}$ are in HP.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.