Solution

158850

First name
Charlotte
School
Harrow
Country
Age
14

For the first problem, the fraction of area that is shaded in blue starts at a half, with the next step being three quarters blue and then half again. This pattern continues. If the pattern continued forever, there would eventually be no obvious difference, but the sequence would carry on forever.

For the geometric patterns below, the area shaded blue is a half, three quarters and obvious fractions. This is because the pattern is made using shapes such as squares and once you split them up, the fraction is easy to work out as they all follow the same steps and it is obvious to work them out.