Proper function a_n for the series a_(n+1) = (a_n)^2?

[biogirl]

The values for the series are given, but I need to find an equation for a_n that satisfies these values. I imagine the answer is obvious but I just can't get it. a_(n+1) = (a_n)^2:

a_0 = 0.5
a_1 = 0.25
a_2 = 0.0625
a_3 = 0.00390625
a_4 = 0.000015258...
etc.

I think this would be a geometric series, and I've tried many possibilities, but none work properly for all a_n. Some help would be wonderful.
Thanks.

 

[stapel]

You refer to "series", which is the sum of the terms in a sequence, but then list sequence terms. Are you finding an expression for the sum of a series, or for the terms of a sequence?

By the way, when you were testing to see if there was a common ratio, what did you notice about the ratios that you obtained?