Math Studies Reality Series Project: Geometric Sequences and Arithmetic Series

By: Maria Alejandra Aparicio

Geometric Sequences

Geometric sequences and the real world: Fianance

We use the following equation:

an=a1 * rn-1

an: last term

a1: first term

r: common ratio

n: position

Geometric Sequence Question

So let’s say you put in $100,000 in your bank account when you are 20. It gains a 3.7% interest annually.

How much money will you have in 1, 2, or 3 years?

If you could live a lot longer than the average human how much would your account have after 467 years?

The Math

The Math 45 years

The Math 467 years!

Arithmetic Series and the Guinness Book of World Records

Brenden Adams is 16 years old and holds the record for being the tallest living teenager.

Brenden’s height is at 2.3 m or 230 cm which by dividing his height by his years we can assume he grew 14.3cm each year.

If this pattern keeps going how tall will he be when he’s 18? What about when he’s 40 or 59 years old?

Using the following formula we can find this out:

Un= u1 + (n-1)d

Un: last term n: number of series

U1: first term d: difference (common difference)

Solving for Brenden’s Height

Bibliography:

Geometric Sequences:

Whiffen, Glen, Marjut Mäenpää, James Foley, Michael Haese, and Sandra Haese. "Sequences and Series." Mathematics for the International Student : Mathematical Studies SL Second Edition. By Mal Coad. 2nd ed. South Australia: Haese & Harris Publications, 2010. 445,475-78. Print.

 

Arithmetic Sequences:

Hanan, Mary. "Meet the Boy Too Big for His Mom's SUV - ABC News." ABCNews.com - Breaking News, Latest News & Top Video News - ABC News. Web. 17 Jan. 2012. <http://abcnews.go.com/Health/MedicalMysteries/story?id=5466774>.

"Tallest Teenager Living (male) - Size - Explore Records - Guinness World Records."Guinness World Records - Home of the Longest, Shortest, Fastest, Tallest Facts and Feats. Guinness World Records. Web. 17 Jan. 2012. <http://www.guinnessworldrecords.com/tallest-teenager-living-(male)/>.