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

Answer 1

Answer: (B)

$\frac{1}{bc},\frac{1}{ca},\frac{1}{ab}$ are in HP

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.