Question

Samuel starts saving for his first car by opening a savings account and depositing $100. He plans to make a deposit every month to continue saving. Each term The amount of money in Samuel's savings account can be modeled by the sequence 100, An An-1 + 75, where n is the number of months since his initial deposit. - Use the drop-down menus below to complete the statements about his savings account growth. The sequence modeling the amount of money in Samuel's savings account is ✓the previous term.​

Answer 1

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.