Problem 235
An Arithmetic Geometric sequence

Given is the arithmetic-geometric sequence u(k) = (900-3k)rk-1.
Let s(n) = Σk=1...nu(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 and are licensed under CC BY-NC-SA 2.0 UK

http://projecteuler.net/problem=235