Question

What number should be added to the numbers 3,7 and 13 so that they are in a continued proportion?

Answer 1

Continued proportion=a:b::bc
ac=bc

Let Number added be=x

Means, (a+x):(b+x)::(b+x):(c+x)

a=3
b=7
c=13
so,

(3+x):(7+x)::(7+x):(13+x)
(3+x)×(13+x)=(7+x)×(7+x)
39+3x+13x+x²=49+7x+7x
+x²

3x+13x+x²-7x-7x-x²=49-39
16x-14x=10 (+x² and-x² will be cut as positive negative)

2x=10
x=10/2
x=5

Number added=5

Hopes it's help
Thanks