martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. she…

martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. she earns interest on her initial deposit. the total amount of money in her savings account at the end of each year is represented by the sequence shown. 100, 105, 110.25, ... which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? o f(n + 1) = f(n) + 5 o f(n + 1) = 5f(n) o f(n + 1) = 1.05f(n) o f(n + 1) = 0.05f(n)

martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. she earns interest on her initial deposit. the total amount of money in her savings account at the end of each year is represented by the sequence shown. 100, 105, 110.25, ... which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? o f(n + 1) = f(n) + 5 o f(n + 1) = 5f(n) o f(n + 1) = 1.05f(n) o f(n + 1) = 0.05f(n)

Answer

Answer:

C. $f(n + 1)=1.05f(n)$

Explanation:

Step1: Find the common ratio

To find the common - ratio between consecutive terms of the sequence $100,105,110.25,\cdots$, divide the second term by the first term. $\frac{105}{100}=1.05$, and $\frac{110.25}{105}=1.05$.

Step2: Recall recursive formula for geometric sequence

For a geometric sequence, the recursive formula is $f(n + 1)=r\times f(n)$, where $r$ is the common ratio. Since $r = 1.05$, the recursive formula for the amount of money in the account is $f(n + 1)=1.05f(n)$.