problem 2 a tank is filled with 100 l of 40 alcohol solution by volume

Question

Problem 2. A tank is filled with 100 L of 40% alcohol solution (by volume). You
repeatedly perform the following operation: Remove 2 L of the solution from the
tank and replace them with 2 L of 10% alcohol solution.
1. Let Cr be the concentration of the solution in the tank after the nth replace-
ment, where Co = 40%. Write the first five terms of the sequence Cn.
2. After how many replacements does the alcohol concentration reach 15%?
3. Determine the limiting (steady-state) concentration of the solution that is ap-
proached after many replacements.