Question

What number should be added to each of number 7,17,47 so that they will be in continued proportion.

Answer 1

Answer:

-2 should be added to each number

Step-by-step explanation:

Let k be the required number to be ladded so that 7, 17, 47 will be in continued proportion

$\implies\:\text{7+k, 17+k, 47+k are in continued proportion}$

$\implies\:\text{7+k:17+k=17+k:47+k}$

$\implies\:\frac{7+k}{17+k}=\frac{17+k}{47+k}$

$\implies\:(7+k)(47+k)=(17+k)(17+k)$

$\implies\:k^2+54k+329=k^2+34k+289$

$\implies\:54k-34k=-329+289$

$\implies\:20k=-40$

$\implies\:k=-\frac{-40}{20}$

$\implies\:\boxed{\bf{k=-2}}$