Insert two geometric means between 4 and 500.

The geometric mean of positive $a$ and $b$ is $G = \sqrt{ab}$, and their arithmetic mean is $A = \dfrac{a + b}{2}$. Always $A \ge G$, with equality only when $a = b$. Two numbers with means $A$ and $G$ are the roots of $x^2 - 2Ax + G^2 = 0$. $n$ geometric means between $a$ and $b$ have ratio $r = (b/a)^{1/(n + 1)}$.