## An Arithmetic Geometric sequence

### Problem 235

Published on Saturday, 7th March 2009, 05:00 am; Solved by 3728; Difficulty rating: 40%
Given is the arithmetic-geometric sequence u(`k`) = (900-3`k`)`r`^{k-1}.

Let s(`n`) = Σ_{k=1...n}u(`k`).

Find the value of `r` for which s(5000) = -600,000,000,000.

Give your answer rounded to 12 places behind the decimal point.