Question

The table below shows the February balance of simple interest savings account each year from 2015 to 2021Year 2015 2016 2017 2018 2019 2020 2021Balance $12,000 14018 16036 18054 20072 22090 241081. Do the balances form an arithmetic or geometric sequence?2. What is the d or the r?3. Write a formula for the balance in the account n years after February 2015.4. Find the sum of the February balances from 2015 to 2032, inclusive.

Answer 1

ANSWER:

1. arithmetic

2. 2018

3.

$b=12000+2018y$

4. $524754

STEP-BY-STEP EXPLANATION:

1.

The balance is an arithmetic sequence, because the increase is constant, that is, the increase from one year to another is always the same.

2.

We calculate the value of d, using the table, subtracting the values, just like this:

$\begin{gathered} d=14018-12000=2018 \\ \\ d=16036-14018=2018 \\ \\ d=18054-16036=2018 \\ \\ d=20072-18054=2018 \\ \\ d=22090-20072=2018 \\ \\ d=24108-22090=2018 \end{gathered}$

The value of d is 2018

3.

Therefore, the formula for the balance in the account n years after February 2015 would be:

$\begin{gathered} b=12000+2018y \\ \\ \text{ where b is the balance in \ and y is years after February 2015} \end{gathered}$

4.

To determine the sum of the values, we must calculate the balance for the year 2032.

In this case y is equal to 17 (2032 - 2015), we replace:

$\begin{gathered} b=12000+2018\cdot17 \\ \\ b=12000+34306=\text{\ }46306 \end{gathered}$

Now, we determine the sum with the following formula:

$\begin{gathered} s=\frac{a_0+a_n}{2}\cdot(n+1) \\ \\ \text{ we replacing} \\ \\ s=\:\frac{12000+46306}{2}\cdot(17+1) \\ \\ s=29153\cdot18 \\ \\ s=524754 \end{gathered}$

So the sum of the February balances from 2015 to 2032 is $524754