BALTIC-WAY 1990 Problem 3

Let $a_{0}>0, c>0$ and

$$a_{n+1}=\frac{a_{n}+c}{1-a_{n} c}, n=0,1, \ldots$$

Is it possible that the first 1990 terms $a_{0}, a_{1}, \ldots, a_{1989}$ are all positive but $a_{1990}<0$ ?