Question

Insert 3 harmonic means between $2$ and $10$.

• A. $\frac{1}{4},\frac{1}{6},\frac{1}{8}$
• B. $\frac{1}{4},\frac{1}{6},\frac{10}{8}$
• C. $4,6,8$
• D. $\frac{2}{4},\frac{1}{6},\frac{1}{8}$

Answer 1

The correct option is A $\frac{1}{4},\frac{1}{6},\frac{1}{8}$

The common difference of AP $=2$
So, the arithmetic sequence is $2,4,6,8,10$.

A sequence of the reciprocals of these terms would be $\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{10}$ which is harmonic.