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Real-Life Scenario: Geometric Sequence

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by

Savannah Cruz

on 5 February 2014

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Transcript of Real-Life Scenario: Geometric Sequence

Real-Life Geometric Sequence
by: Savannah Cruz

The amount of money in your account increases by 1% each month according to the previous month. This monthly increase creates a geometric sequence of 100, 101, 102.01, 103.0301, 104.060401,....
Equations
Why this scenario?
I chose this scenario because this is something I deal with in my day to day life. The question we did in class, about a toy's sales decreasing by 10% each year, pushed me toward this scenario. Of course, I changed it from sales to interest and to monthly interest instead of yearly decrease. Also, I thought this scenario would be easier to understand and more relevant to what is going on in our lives at the time.
Research Sources
The Series and Sequences Videos are where I obtained the information for the equations. The sales question that we did in class as a group helped me to decide my scenario.
Savings Account Scenario
You are starting a savings account for college. This savings account gains 1% interest per month. you start with $100 in the account so that by the start of month 2 you have $101, by the start of month 3 you have $102.01, and so on increasing 1% each month according to what the previous month was for the rest of the life of the account as long as no money is deposited or withdrawn from the account.
2004
2007
2013
2010
2001
Month 1
Start with $100:
Month 2
Start with $101:
Month 3
Start with $102.10:
Month 4
Start with $103.0301:
Month 5
Started with $104.060401:
Summation Notation
Explicit Formula
Recursive Formula
a = 100
1
a = (a ) (1.01)
n
n-1
a = 100
1
a = (100) (1.01)
n
n-1
Full transcript