Some sequences and series info. and examples. This show includes fractals. It was created as a final project for my math class.

1. Sequences and Series
By: semba04
June 1/09

2. Popular Ways to Solve Sequence
Questions
Excel (my favorite, so I‟ll probably focus on it)
Graphing Calculator
Shodor.org
By Hand

3. Example: If there are 986 rooms rented
out of an apartment, 12% move out and
122 move in, how many will be rented out
the next year? When the number of
people level out in the apartment (when
their is a constant number), how many
people will that be?
We‟ll do it on excel first

4. First, we should (should be apparent) put
the years in. There is a year 0 because we
are starting with the numbers that will
affect the next year.
Note: You can very easily pull down values. Click
on a cell and move your cursor to the bottom
right hand corner until it turns to a solid cross.
Then you can pull down that box to copy the
format.

5. Note: When you want to enter an
equation you have to put an = in
front of it.
The next thing I did was put a
header in for the “12% move out”
and I just put 122 beside the year
because that‟s how many move
out.
All the values that we are using to
calculate are in a row beside the
year.
As you can see I‟ve inserted the
equation that will calculate the
amount of people that will move
out (since our „units‟ are people).
Press enter and you‟ll get how
many people moved out.

6. Next I copied the format for
the 122 people and the
percent that moved out (used
the little cross thing and
dragged it to the bottom).
Then I inserted the equation
that will get the number of
people for out first year (we
have 986 people, 12% move
out and 122 move in).
Note: When forming an
equation and you want to
use a value from another
cell you can click on the
cell you want the value
from even if your in the
middle of making an
equation (you can see the
dotted line around E3 – I
used for my equation.)

7. This should be a note but, it‟s
important with excel. You have to
be careful when copying the
formatting of cells. The cell you
want to copy for the total number
of people is C4 because that is the
cell with your equation in it.
The answer for the first part
of the question is 990 people
(round because your not
going to have half a person
occupy a suite).

8. The second part of the question
can easily be done by dragging
down all your values until the
number of people remain
relatively constant.
Note: You can‟t just highlight
everything you just did and drag
it down , you have to go down
the individual columns.
The answer will be very close to
1016 people.

9. Here is a clipping from Shodor.org. The values are http://www.shodor.org/i
easy enough to understand, but I find this to be nteractivate/activities/Se
limited compared to excel. If you really wanted to quencer/
find out how this app. works you should go and
play around with it.

10. You can probably tell how this
would go if you did it by hand or on
the home screen of you TI
calculator. You would find 12% of
986. Then minus the 12% and add
122. From that answer you would
repeat the process.
There is a sequence mode on your
TI. I know you can start it by going
to MODE and changing FUNC to
SEQ. This allows you to make a
graph.
Pg. 117-125 in this book shows you
how to make a sequence graph.

11. Example:
In October an oil well in Alberta
produced 80m³ of oil. Each month the
well produces 1.3% less oil than the
previous month.
A) In total, how much oil will be produced in a six
month period beginning October 1?
B) Once the well production drops below 60m³
per month it is not profitable to operate the
well. In which month will it no longer be
profitable to operate the well?
The answer is on the next slide.

12. You can see how I
bolded the sixth
month. Beside that
month I made an
equation that adds
the oil produced over
the six months. The
equation I used was:
=sum(C19:C24)
Note: All I really
typed to get that
equation was =sum,
then I selected the
cells I wanted to add.
Note: You can drag down months.
To get B I dragged down all my values until
the amount of oil produced dropped below
60m³. The well is not profitable after July.

13. Fractals
A geometric pattern that is repeated at ever
smaller scales to produce irregular shapes
and surfaces that cannot be represented by
classical geometry.
-dictionary.com

15. A fractal question may look like this:
Generation Generation Generation
1 2 3 Find the perimeter of
the 4th Generation.
Here is what you might want to do:
Generation Number of sides Length of sides Perimeter I times the number of
1 3 27 81 sides by the side length
2 (3*4) = 12 (27/3) = 9 108 to get the perimeter of
3 (3*4)*4 = 48 (27/3)/3 = 3 144
the generation.
4 ((3*4)*4)*4 = 192 ((27/3)/3)/3 = 1 192

16. Online fractal applications from
Shodor.org:
Hilbert Curve Generator Sierpinski's Triangle Sierpinski‟s Carpet
The Mandelbrot Set
Koch‟s Snowflake Julia Sets

17. And the Chaos Game:
Fun version here: