Question

The sixth H.M between $3$ and$\frac{6}{13}$ is

• A. $\frac{63}{120}$
• B. $\frac{63}{12}$
• C. $\frac{126}{105}$
• D. $\frac{120}{63}$

Answer 1

The correct option is A

$\frac{63}{120}$

Explanation for the correct option.

Find the required H.M between given numbers.

Given numbers: $3$ and$\frac{6}{13}$

We know that for H.M, $x_n=\frac{(n+1)ab}{(na+b)}$.

We have $a=3,b=\frac{6}{13}$ and $n=6$.

By substituting the value, we get

$$\begin{gathered} x_6=\frac{\left((6+1)3\times \frac{6}{13}\right)}{\left(6\times 3+{\displaystyle \frac{6}{13}}\right)} \\ {x}_6=\frac{\left(7\times 3\times \frac{6}{13}\right)}{\left(18+{\displaystyle \frac{6}{13}}\right)} \\ {x}_6=\frac{{\displaystyle \frac{126}{13}}}{{\displaystyle \frac{240}{13}}} \\ {x}_6=\frac{126}{240} \\ {x}_6=\frac{63}{120} \end{gathered}$$

Therefore, the sixth H.M between $3$ and$\frac{6}{13}$ is $\frac{63}{120}$.

Hence, option $A$ is the correct answer.