Question

Five numbers are in continued proportion whose second term is 6 and fourth term is 54. Find the numbers.

• A. 2, 6, 18, 54, 162
• B. 2, 6, 18, 54, 16
• C. 2, 6, 18, 54, 1
• D. 2, 6, 18, 5, 162

Answer 1

The correct option is A 2, 6, 18, 54, 162

Given,
$5$ numbers are in continued proportion.
Let the continued proportion be $a,ak,a{k}^2,a{k}^3,a{k}^4$

Given,
$ak=6$ and
$a{k}^3=54$

Now,
$a{k}^3=54$
$=>ak\left(k^2\right)=54$
$=>6\left(k^2\right)=54$
$=>\left(k^2\right)=9$
$=>k=3$
$\therefore a=\frac{6}{3}$
$=2$

$\therefore$ The continued proportion is $2,6,18,54,162$