题目235：一种算术几何序列
An Arithmetic Geometric sequenceGiven 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.
题目：
假设算术几何序列 u(k) = (900-3k)rk-1。
设 s(n) = Σk=1...nu(k).
求 r 的值，使得 s(5000) = -600,000,000,000。
给出你的答案并精确到第 12 位小数。
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