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

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 is f(n+1)= 1.05 f(n)

Solution:

Given that,

The total amount of money in Martina savings account at the end of each year is represented by  the sequence shown as:

100, 105, 110.25, ...

The above sequence is a geometric sequence

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r

The common ratio is:

Here in 100, 105, 110.25

Or,

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

The recursive formula is given as:

Let f(n) be the total amount of money earned in previous year

Let f(n + 1) be the total amount of money earned in any year

So,

Thus the recursive formula is found

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