Question

a cask containing 20 liters of wine was emptied of one-fifth of its contents and then filled with water. if this is done 20 times, how many wine will remain in the cask?

Answer 1

after each drain-fill cycle, there is 0.8 the amount of wine as before.

So, after 20 cycles, the wine remaining is

20(0.8^20) liters

Answer 2

First term=20-1/5(20)=16
Second term= 12.8
r=4/5
An=A1 (r^n-1)
A20=16(4/5)^20-1
A20=0.23058 Liters