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? f(n + 1) = f(n) + 5 f(n + 1) = 5f(n) f(n + 1) = 1.05f(n) 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? f(n + 1) = f(n) + 5 f(n + 1) = 5f(n) f(n + 1) = 1.05f(n) f(n + 1) = 0.05f(n)

Answer

Answer:

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

Explanation:

Step1: Identify the type of sequence

The sequence $100,105,110.25,\cdots$ is a geometric - sequence.

Step2: Calculate the common ratio

The common ratio $r=\frac{105}{100}=1.05$.

Step3: Recall the recursive formula for a geometric sequence

For a geometric sequence, the recursive formula is $f(n + 1)=r\times f(n)$. Here $r = 1.05$, so $f(n + 1)=1.05f(n)$.