This question doesn't support checking answers.

235. An Arithmetic Geometric sequence

Given is the arithmetic-geometric sequence u(k) = (900-3k)r^k-1.
Let s(n) = Σ_k=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.