Question

Check whether the following numbers are in continued proportion.

(i) 2, 4, 8 (ii) 1, 2, 3 (iii) 9, 12, 16 (iv) 3, 5, 8

Answer 1

The numbers a, b, c are in continued proportion if $\frac{a}{b}=\frac{b}{c}$.

(i)
$$\begin{gathered} \frac{2}{4}=\frac{1}{2} \\ \frac{4}{8}=\frac{1}{2} \end{gathered}$$
Since $\frac{2}{4}=\frac{4}{8}$, so the numbers 2, 4, 8 are in continued proportion.

(ii)
Since $\frac{1}{2}\ne \frac{2}{3}$, so the numbers 1, 2, 3 are not in continued proportion.

(iii)
$$\begin{gathered} \frac{9}{12}=\frac{3}{4} \\ \frac{12}{16}=\frac{3}{4} \end{gathered}$$
Since $\frac{9}{12}=\frac{12}{16}$, so the numbers 9, 12, 16 are in continued proportion.

(iv)
Since $\frac{3}{5}\ne \frac{5}{8}$, so the numbers 3, 5, 8 are not in continued proportion.