Question

Theo has $125 dollars in his savings account. He requests that $10

dollars a week be deducted from his paycheck and added to the savings
account.
Find the recursive rule that models the total amount in Theo's savings
account at the end of each week.

Answer 1

The recursive rule that models the total amount in Theo's savings account at the end of each week starts with an initial amount of $125 and adds $10 every week, expressed as Sn = Sn-1 + $10, where Sn is the amount in week n.

Step-by-step explanation:

To find the recursive rule that models the total amount in Theo's savings account at the end of each week, we can define the initial amount and the change that occurs each week as a function of the previous week. Let Sn be the savings amount in the n-th week, and Sn-1 be the amount in the previous week.

The initial amount, which is the scenario when n = 0, is given as S0 = $125. Theo adds $10 to his savings account every week, so the recursive formula for any week n > 0 is Sn = Sn-1 + $10.

In summary, the recursive rule for Theo's savings account is:

• Initial amount (base case): S0 = $125
• Recursive step (for n > 0): Sn = Sn-1 + $10