Question

Show that $6,36,216$ are in the proportion.

Answer 1

Three numbers a, b and c are in continued proportion if, $a:b::b:c$
$\Rightarrow \frac{a}{b}=\frac{b}{c}$
Now, take given numbers as $a=6,b=36,c=216$
Consider $\frac{a}{b}=\frac{6}{36}$
$\Rightarrow \frac{a}{b}=\frac{1}{6}$......(i)
Similarly, consider $\frac{b}{c}=\frac{6}{216}$
$\Rightarrow \frac{b}{c}=\frac{1}{6}$......(ii)
From equation(i) and (ii), we get $\frac{a}{b}=\frac{b}{c}$
Thus, the numbers $a=6,b=36,c=216$ are in proportions.

Hence, the given numbers are in proportion.