Question

If first , second and fourth terms of a proportion are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{6}$ respectively, find its third term.

Answer 1

First, second and fourth terms of a proportion are given $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{6}$ respectively.

Assume third term $=x$

Therefore, $\frac{1}{2},\frac{1}{3},x,\frac{1}{6}$ are in proportion.

We know that,

Product of Means$=$ Product of extremes

$$\begin{gathered} \frac{1}{3}\times x=\frac{1}{2}\times \frac{1}{6} \\ x=\frac{3}{2\times 6}=\frac{1}{4} \end{gathered}$$

Hence, third term is $\frac{1}{4}$