Question

Find the value of $p$, if $p,6and9$ are in continued proportion.

Answer 1

Continued proportion:

Given: $p,6,and9$ are in continued proportion.

We know, three numbers are said to be in continued proportion, if the ratio of first to second is the same as that of second to third i.e, $a:b::b:cor\frac{a}{b}=\frac{b}{c}$

So, $\frac{p}{6}=\frac{6}{9}$

$$\begin{gathered} Productofmeans=Productofextremes \\ \Rightarrow p\times 9=6\times 6 \\ \Rightarrow p=\frac{6\times 6}{9} \\ \Rightarrow p=\frac{36}{9} \\ \Rightarrow p=4 \end{gathered}$$

Thus, the required value of $p=4.$