Question

Five numbers are in continued proportion. The first number is 5 and the last number is 80. Find the third number.

Answer 1

Let the numbers in continued proportion be a, ak, $a{\text{k}}^2$, $a{\text{k}}^3$, $a{\text{k}}^4$.
Given first term is 5 so, a=5 and last term is 80 so, $a{\text{k}}^4$=80.
$\Rightarrow a{\text{k}}^4=80$
$\Rightarrow 5{\text{k}}^4=80$
$\Rightarrow {\text{k}}^4=16$
$\Rightarrow \text{k}=2$
Hence the five numbers are 5, 10, 20, 40, 80. The third number will be 20.