find function for series that describes multiple steals from target

Question

I have a problem where I want to know the total amount of points I take away from a target, when I take away x times a% of points from the target. The series that does that is described as follows:

x0 = a
x1 = (1-x0)*a + x0
x2 = (1-x1)*a + x1
x3 = (1-x2)*a + x2
x4 = (1-x3)*a + x3

is there a function f(x) that gives me the total amount of points taken away given the amount of hits?

Answer 1

asking the question sometimes directly leads to the answer. The answer:

$$f(x) = 1-(1-a)^x$$

turns out it is a simple multiplication (doh)