I'm trying to use the following sequence as a scoring system, but couldn't find the explicit formula:
\begin{equation} \begin{cases} a_n= a_{n-1}-200*0.75^{n-2}\\ a_1=1000 \end{cases} \end{equation}
This generates the following values:
\begin{array}{|c|c|} \hline n & a_n \\ \hline 1 & 1000 \\ \hline 2 & 800 \\ \hline 3 & 650 \\ \hline 4 & 537.5 \\ \hline \end{array}
The sequence is designed to award an points to the nth ranked player.
What would the explicit formula be, and what is this kind of sequence called?