Sequences and Series

Create Your Own Reality Series!

Sequences and Series - Project

Due:______

Would you like to create your own reality series? What would you do?

What kinds of people or things might be involved? Maybe you couldfocus on the number of seats in a theater or the distance a ball travels when it bounces. What’s that? You thought this project was going to be about a televisionreality series? Sorry, this project focuses on arithmetic and geometric series(and sequences). In some cases, this might be more interesting than whatyou find on television!

Arithmetic and geometric sequences and series arise in many situations.

• Depreciation of a car can be an arithmetic sequence if the cardepreciates by a certain dollar amount every year. The sequencebecomes geometric if the car depreciates by a percentage eachyear.

• Investments can be represented by arithmetic sequences or series ifa set dollar amount is added at given intervals.

• If salary increases are given at a particular percentage per year, ageometric sequence can be used.

• It is also interesting to calculate the distance traveled by a ball as itbounces. If a ball bounces to 80% of its previous height, you can usethis as the common ratio to evaluate the geometric series. Be sureto take into account the distance up and down between eachbounce.

• An athlete in training might add a set distance to each workout. Anarithmetic series can be used to calculate the total distance afterone month of training.

In our studies of Sequences and Series, we discussed many topics about arithmetic andgeometric sequences and series. You have seen how to find the nth term, write explicit and recursive formulas and find the sum of each type ofseries. You learned that a geometric series can be finite or infinite anddepending on the common ratio, the series might have a partial sum or itmight not. Now you can use these concepts in real-life scenarios.

Your task is to choose situations that can be represented by arithmetic or geometric sequences and series. Choose onesituation that is arithmetic and one that is geometric. If you wish, searchthe Internet for real-life scenarios to help you get started. If you choose touse something you find during your research, be sure to change thenumbers to make your application unique. Find something fun that youfind interesting. Whether it is investment related, physics related, orsomething else entirely, choose what interests you most to make your ownreality series!

The creation of a well-developed Reality Series Project should have:

1. Real-life series: Choose real-life situations which use arithmetic orgeometric sequences and series. You must have at least one arithmetic and geometric for this project. Write a description of each scenario.

1. Research: Cite any research you did to discover the real-lifeapplications of sequences and series. If you created the real-lifeapplications yourself, explain your thinking. If you used ideas fromother sources, show how you changed the terms, commondifference, or common ratio to make your application unique.

1. Diagrams or pictures: Include a diagram or picture of the situationsyou have chosen. Write out the 1st several terms and usepictures to represent what is taking place. For example, if a ball isbouncing you might want to show the distance traveled in the 1stseveral bounces.

1. Formulas: Write the recursive and explicit formulas for eachsequence in the series. Then write the series using summationnotation.

1. Presentation: Create a visual to display your series. Suggestions of visuals include but are not limited to: create a poster, a pamphlet, a power point presentation, or a website. If you create an electronic visual a copy must be printed and turned in to be graded.

Your project will be graded using the following grading rubric: