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)

The correct option will be:  

Explanation

The total amount of money in her account at the end of each year...

100,  105,  110.25, ........

The above sequence is a geometric sequence as there is a common ratio in between any two consecutive terms. So the common ratio

This means , any term in the sequence is 1.05 times the previous term.

So, the recursive formula which can be used to determine the total amount of money earned in any year based on the amount earned in the previous year will be:

Step-by-step explanation:

Given : The total amount of money in Martina's savings account at the end of each year is represented by the sequence :

100, 105, 110.25, ...

It is an geometric sequence because the ratio of any two consecutive terms is same.

i.e.

So the common ratio =

Recursive formula for geometric sequence :

Put r= 1.05, we get

The 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 :