Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An...
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Transcript of Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An...
![Page 1: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/1.jpg)
MSP SI 2007 Sequences Joan Carter
Sequences Sequences
![Page 2: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/2.jpg)
MSP SI 2007 Sequences Joan Carter
Sequences
What is a sequence?
An ordered list of objects (or events)
Like a set, it contains members (called elements or terms) and the number of terms is called the length.
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MSP SI 2007 Sequences Joan Carter
Workshop Objectives
You will be able to identify various sequences and use GeoGebra to:
• Graphically represent sequences• Use the sequence command to
create lists of objects
• Use the element command to find the nth term of a sequence• Use the segment command to
create line designs
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MSP SI 2007 Sequences Joan Carter
Number Patterns
Find the next two terms of each sequence. Describe how you found each term.
0, 1, 3, 6, 10, 15, ___, ___
11, 22, 33, 44, 55, ___, ___
5, 8, 7, 10, 9, 12, 11, __,__
6666 7777
2121 2828
1414 1313
Slide Courtesy of Guy Barmoha
![Page 5: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/5.jpg)
MSP SI 2007 Sequences Joan Carter
Sequences
(a,ar1,ar
2,ar
3...)
F(n) :0
1
F (n 1) F(n 2)
Examples Sequence
Notation
(a1,a2,a3,...an )
(1,2,3,...)
(1,4,7,...)
arithmetic
(2,4,8,...)
geometric
(1,1,2,3,5,8...)
Fibonacci
(1,1
2,1
4,1
8,...)
![Page 6: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/6.jpg)
MSP SI 2007 Sequences Joan Carter
Arithmetic Sequences
Sequence of numbers where any 2 successive members have a common difference
Example:( 0, 1, 2, 3, 4 )
+ 1 +1 +1 +1
![Page 7: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/7.jpg)
MSP SI 2007 Sequences Joan Carter
Arithmetic Sequences
Sequence of numbers where any 2 successive members have a common difference
Example:( 0, 3, 6, 9, 12 )
+ 3 +3 +3 +3
![Page 8: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/8.jpg)
MSP SI 2007 Sequences Joan Carter
What would these sequences look like if we graphed them?
X Y
0 0
1 3
2 6
3 9
4 12
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MSP SI 2007 Sequences Joan Carter
What would these sequences look like if we graphed them?
X Y
0 1
1 4
2 7
3 10
4 13
A line?Possibly, but we need to checkit out! GeoGebra will help us.
![Page 10: Joan Carter MSP SI 2007Sequences Sequences. Joan Carter MSP SI 2007Sequences What is a sequence? An ordered list of objects (or events) Like a set, it.](https://reader034.fdocuments.in/reader034/viewer/2022051401/5697bfbc1a28abf838ca1869/html5/thumbnails/10.jpg)
MSP SI 2007 Sequences Joan Carter
What would these sequences look like if we graphed them?
X Y
0 1
1 4
2 7
3 10
4 13
seq_line1.ggb
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MSP SI 2007 Sequences Joan Carter
Sequences
X Y
0 1
1 4
2 7
3 10
4 13
Yes, this is a linear sequence!How would we find the equationof the line without graphing?
Common difference = 1
Common difference = 3
Slope= change y = 3
change x 1 y = 3 x + ? y = 3 x + 1
y = m x + b
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MSP SI 2007 Sequences Joan Carter
Number Sequences
Term
Value
1 2 3 4 5 6
4 7 10 13 16 19
7
What is the 7th term of this sequence?
What is the 200th term of this sequence?
22
… 200
… ?
Slide Courtesy of Guy Barmoha
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MSP SI 2007 Sequences Joan Carter
Number Sequences
Term
Value
1 2 3 4 5 6
4 7 10 13 16 19
7
What is the 7th term of this sequence?
What is the 200th term of this sequence?
22
… 200
… ?
22
seq_line2.ggb
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MSP SI 2007 Sequences Joan Carter
To find the nth term algebraically, usean = a1 + (n-1) d
a1 = initial term, d = common difference
.
Sequences
What equation is this? Slope-Intercept Form y = 3x + 1
y = 3(200) + 1 y = 601
Term
Value
1 2 3 4 5 6
4
7 … 200
7 19161310 …22 ?
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MSP SI 2007 Sequences Joan Carter
Sequences: GeoGebra Review
To create a list of objects: Use sequence command: Sequence[expression e, variable i, number a, number b]
To find the nth element in a list: Use element command: Element[List L, number n]
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MSP SI 2007 Sequences Joan Carter
Sequences: Segments in GeoGebraSlide background resembles Bezier curve
Dr. Pierre Bezier (1910-1999)
Engineer for French automaker
“Best fit” curve for manufacturing
Used in computer graphics
He used 4 points; We’ll use 3.
seq_line_art1.ggb
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MSP SI 2007 Sequences Joan Carter
Segment Sequences
Markus’line art tool seq_line_art2.ggb
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MSP SI 2007 Sequences Joan Carter
Sequences of Segments on a Circleseq_circle_segments1.ggb
seq_circle_segments3.ggb
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MSP SI 2007 Sequences Joan Carter
Sequences
• SSS: MA.D.1.3.1, MA.D.2.4.1
• All files will be posted on tiki at
http://nsfmsp.fau.edu/tiki/tiki-index.php
• Contact me at [email protected]
• Special thanks to Dr. Markus Hohenwarter
and Guy Barmoha, MST.