Problem 235

An Arithmetic Geometric sequence

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.

**
These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
**