x increases with 125% each week, what is x week n?

Question

x has the value 1.

How would I calculate the accumulative value of x for a certain week, if x increases with 125% each week?

Answer 1

At the end of first week, $x$ becomes $1.25$

At the end of second week, $x$ becomes $1.25^2$

At the end of third week, $x$ becomes $1.25^3$

In general, at the end of $n^{th}$ week, $x$ becomes $1.25^n$

Answer 2

Hint: Calculate the amount that $x$ increases in week one, two, three and maybe four. Try to see a pattern in terms of an exponent that reflects which week you are in. Once you have that pattern, generalize the answer in terms of $n$.