Question

Jill has 64 ounces of lemonade. Each day, her brother drinks 16 ounces. Then at the end of each day Jill adds 25% of the remaining total back into the lemonade container. Which recursive formula models the number of ounces of lemonade in the container, an, at the end of the nth day?

Answer 1

Let a0 = 64 (initial amount). For n ≥ 1,
an = 1.25( a_{n-1} − 16 )
which can be written as
an = 1.25 a_{n-1} − 20.

(For example, a1 = 1.25(64 − 16) = 60.)