By: Anthony Bradley

This project is intended to show the difference between arithmetic and geometric sequences and how they can be applied in a real life situation. In this project I will show a real life example of an arithmetic and geometric sequence and all its processes. I will also include my research and diagrams/ graphs to support my final answers.

An arithmetic sequence is one in which each member of the sequence has a constant factor added or subtracted to the next member. Example: 2,4,6,8,10,12,14...

A geometric sequence is one in which each member of the sequence is multiplied or divided by a constant factor to get the next member. Example: 2,6,18,54,162,486,1458...

My real life arithmetic sequence is the leasing of a car.

Automobile leasing is based entirely on the concept that you pay for the amount by which a vehicle's value depreciates during the time you're driving it.

Vehicles with a lower depreciation rate, make the best lease deals.

Example: I will be leasing a Toyota Yaris to a costumer and he will have to sign a leasing contract.

Contract: Constant payments of $100 per month for a year.

My real life geometric sequence will be the depreciation by a percentage of a car each year for 5 years.

A car starts to depreciate as soon as you drive it out of the parking lot. This happens because when you by a new car, you are paying the retail price of the vehicle. The instant you drive away from the dealership, the value of the car becomes wholesale. Meaning, if you were to try and sell your car back to the dealer, you would only be entitled to the wholesale price. 

Wholesale price: A wholesale price is the price offered to purchasers of manufactured goods or to commercial sellers in many cases.

Retail price: The price of a product charged in a store to customers.

Year Appreciation price ($)

2012 50,000

2013 65,000

2014 84,500

2015 109,850

2016 142,805

2017 185,646.5

2018 241,340.4

What problems did you encounter as you completed the project?1) I had trouble choosing a geometric example because at first I decided to do the

depreciation percentage of a car every year but then found out that after a certain amount of years I would end up with a negative number which wouldn’t work.

2) I had to research some terms I did not know like retail and wholesale price, and leasing for example.

3) I had some trouble with the equations for the geometric example. How did you solve these problems? 1) Since depreciation wouldn’t work I decided to do the opposite, the appreciation of a

vintage car over the years. This worked just fine. 2) I used the internet as my research tool and I understood these terms perfectly 3) With the help of Ms. Rosanna I was able to apply the formulas to the problem and

show my work effectively. What was your favorite part of the project?

My favorite part of the project was researching about real life geometric and arithmetic sequences. I also enjoyed making the tables and graphs to visually show my results. I think that those graphs are very helpful to perceive the pattern and relationship. The research was also very interesting and I learned many things about cars.

What did you learn from this project? I learned many good things form this project. First of all I learned new things I never knew before about leasing, car depreciation and I kept on practicing my math skills by using the formulas I used. I learned that arithmetic and geometric sequences are everywhere in real life and we can relate them to almost anything going on in the real world.

http://www.money-zine.com/Calculators/Auto-Loan-Calculators/Car-Depreciation-Calculator/

http://www.bankrate.com/brm/news/auto/20011226a.asp

http://www.regentsprep.org/Regents/math/algtrig/ATP3/Recursive.htm

http://answers.yahoo.com/question/index?qid=20080909094817AA3WWP7

http://www.leaseguide.com/lease07.htm http://answers.yahoo.com/question/index?

qid=20061104101604AA7pE6R http://answers.yahoo.com/question/index?

qid=20080225135346AAIgnqI