Geometric
Geometric
Application
Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day, etc. If the daily wage continues to double, what is your total income for working 31 days?
,
and
![GeoApp1-5 GeoApp1-5](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-5.png)
![GeoApp1-6 GeoApp1-6](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-6.png)
![GeoApp1-7 GeoApp1-7](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-7.png)
Step 1. Write a geometric sequence to represent the situation.
1, 2, 4, 8, 16 …
Step 2. Determine a1, r and n.
![GeoApp1-1 GeoApp1-1](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-1.png)
![GeoApp1-2 GeoApp1-2](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-2.png)
![GeoApp1-3 GeoApp1-3](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-3.png)
Step 3. Determine the general formula for the sequence .
![GeoApp1-4 GeoApp1-4](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-4.png)
![GeoApp1-5 GeoApp1-5](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-5.png)
Step 4. To find the series, substitute and solve.
![GeoApp1-6 GeoApp1-6](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-6.png)
![GeoApp1-7 GeoApp1-7](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-7.png)
![GeoAPp1-8 GeoAPp1-8](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-8.png)
![GeoApp1-9 GeoApp1-9](https://claregladwinresd.glk12.org/pluginfile.php/1012/mod_book/chapter/607/Sequence_and_Series/Images/GeoApp1-9.png)
The total pay for 31 days is 2,147,483,647¢ or $21,474,836.47.