Question

Five numbers are in continued proportion where the first term is 1 and last term is 256. Find the numbers.

• A. 1, 4, 16, 64, 256
• B. 1, 4, 16, 64, 25
• C. 1, 4, 16, 64, 2
• D. 1, 4, 16, 6, 256

Answer 1

The correct option is A 1, 4, 16, 64, 256

Given,
$5$ numbers are in continued proportion.
Let the continued proportion be $a,ak,a{k}^2,a{k}^3,a{k}^4$
Given,
$a=1$ and
$a{k}^4=256$
Now,
$a{k}^4=256$
$=>\left(1\right)\left(k^4\right)=256$
$=>k^4=(4{)}^4$
$=>k=4$
$\therefore$ The continued proportion is $1,4,16,64,256$