Answer: The sequence modeling the amount of money in Samuel’s savings account is a recursive sequence. Each term in the sequence is determined by adding $75 to the previous term. The first term in the sequence is $100, representing Samuel’s initial deposit. After n months, the amount of money in Samuel’s savings account can be calculated using the formula An = An-1 + 75, where An represents the amount of money in his account after n months and An-1 represents the amount of money in his account after n-1 months.
For example, after 1 month, the amount of money in Samuel’s savings account will be A1 = A0 + 75 = 100 + 75 = $175. After 2 months, the amount of money in his account will be A2 = A1 + 75 = 175 + 75 = $250. And so on.