If each term of a geometric progression $a_1, a_2, a_3, \ldots$ with $a_1 > 0$ and $a_2 \neq a_1$, is the arithmetic mean of the next two terms and $S_n = a_1 + a_2 + \ldots + a_n$, then $S_{20} \cdot S_{18}$ is equal to: