Question

Insert 3 harmonic means betwwen 5 and 9.

• A. $6,7,8$
• B. $\frac{45}{8},\frac{45}{7},\frac{45}{6}$
• C. $\frac{8}{45},\frac{7}{45},\frac{6}{45}$
• D. $\frac{1}{8},\frac{1}{7},\frac{1}{6}$

Answer 1

The correct option is B $\frac{45}{8},\frac{45}{7},\frac{45}{6}$

Let $5,h1,h2,h3,9$

First finding $h2$:

$\therefore h2=\frac{2\times 5\times 9}{5+9}=\frac{45}{7}$

Now, finding H.M. between $5$ and $h2$, i.e., $h1$

$\therefore h1=\frac{2\times 5\times \frac{45}{7}}{5+\frac{45}{7}}=\frac{45}{8}$

Now, finding H.M. between $h2$ and $9$, i.e., $h3$

$\therefore h3=\frac{2\times \frac{45}{7}\times 9}{\frac{45}{7}+9}=\frac{45}{6}$

$\therefore$ Harmonic series: $5,\frac{45}{8},\frac{45}{7},\frac{45}{6},9$