When your doing tax the tax is 9.25 you divide that by 100
the add that to your price then 12.5 divided by 100 and subtract that from what you ended up with so you should come out with a total of 4.22
From 100 to 80 is 8/10, so the recursive formula is
an=a(n-1)*1/8
or
an= a1*1/8(n-1)
an=a1*(n-1)/8

This is a geometric series with a common ratio between successive terms that is less than 1 in absolute value. This means the series will converge. The value of the sum is

.