Takuya's parents gave him $100 dollars as a birthday gift. Since he loves board games, he spent $20 out of his present on board games at the end of each month until his money ran out.

Let f (n) be the amount of money that remained from Takuya's present during month n where n=1 represents the month he received his present.

f is a sequence. What kind of sequence is it?

The expression that represents the amount of money Takuya has over the months is "f (n) = f (1) + (n - 1) * r" and the sequence is an arithmetic sequence.

Step-by-step explanation:

Since the initial amount of money Takuya had was 100 dollars and he spent 20 dollars every month, then each element of the sequence is related to it's prior by the sum of - 20, therefore it's a arithmetic sequence. In order to calculate the "nth" term of a sequence like this we need to apply the following formula:

f (n) = f (1) + (n-1) * r

f = {100, 80, 60, 40, 20, 0}