--description--

Given is the arithmetic-geometric sequence $u(k) = (900 - 3k)r^{k - 1}$.

Let $s(n) = \sum_{k=1 \ldots n} u(k)$.

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

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

--hints--

arithmeticGeometricSequence() should return 1.002322108633.

assert.strictEqual(arithmeticGeometricSequence(), 1.002322108633);

--seed--

--seed-contents--

function arithmeticGeometricSequence() {

  return true;
}

arithmeticGeometricSequence();

--solutions--

// solution required