Luiza's savings account had $50 in its first year. Each year since then, her account accumulated interest
amounting to 15% of the balance in the previous year.
Let g(n) be Luiza's account balance at the nth
year of the saving.
g is a sequence. What kind of sequence is it?

50(1.15)^n-1

Step-by-step explanation:

1. Let's consider the first three terms of g(n) to get a sense of how the function values change as n increases.

2. The first term is Luiza's account balance at the first year of the saving, which is the initial amount she deposited. We know this to be $50.

The second term is Luiza's account balance at the second year. Since the account accumulated 15% each year, it was 1.15 times the balance in the first year, which is $50*1.15=$57.50.

The third term is Luiza's account balance at the third year. Again, this is 1.15 times the balance of the year before that, which is $57.50*1.15=$66.125.

To summarize:

g(1)=50   g(2)=50*1.15   g(3)=50*1.15*1.15

We can see that each term is 1.15 times its preceding term. There is a constant ratio between consecutive terms. Therefore, this is a geometric sequence.

3. We can write an explicit formula for this geometric sequence using the form A*B^n-1. In this form,  A,  is the first term and B is the common ratio. What are the appropriate values for our case?

The first term is Luiza's initial deposit, which is $50.

The common ratio corresponds to the percentage of accumulated interest. Since that percentage is 15%, the common ratio is 1.15.

4. In conclusion, g is a geometric sequence.

An explicit formula for the sequence is g(n)=50*1.15^n-1

Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.

g

step-by-step explanation: