Question

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. $\frac{1}{b}, \frac{1}{c}, \frac{1}{a}$ are in $HP$

Answer 1

Answer: (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 $HP$.