Solve a daily retention recurrence

Celine takes $500$ mg of Vitamin C once daily. The model assumes $20\%$ remains immediately before the next day’s pill. Let $x_n$ be the amount immediately after dose $n$, with $x_1$ immediately after the first dose.

(i) Write a recurrence. (ii) Show $x_n=(0.2)^{n-1}(x_1-625)+625$. (iii) Deduce the limit.