Sequences in GeoGebra

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# Sequences in GeoGebra - PowerPoint PPT Presentation

Sequences in GeoGebra. Sequences. 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 . Workshop Objectives.

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Presentation Transcript
Sequences in GeoGebra

Sequences

Sequences

Sequences

What is a sequence?

An ordered listof objects (or events)

• Like a set, it contains members
• (called elements or terms) and the
• number of terms is called the length.

Sequences

Workshop Objectives
• You will be able to identify various sequences and use GeoGebrato:
• 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

Sequences

Number Patterns

Find the next two terms of each sequence. Describe how you found each term.

11, 22, 33, 44, 55, ___, ___

66

77

21

28

0, 1, 3, 6, 10, 15, ___, ___

14

13

5, 8, 7, 10, 9, 12, 11, __,__

Sequences

Slide Courtesy of Guy Barmoha

Sequences

Sequences

Arithmetic Sequences

Sequence of numbers where any 2 successive members have a common difference

Example:

( 0, 1, 2, 3, 4 )

+ 1 +1 +1 +1

Sequences

Arithmetic Sequences

Sequence of numbers where any 2 successive members have a common difference

Example:

( 0, 3, 6, 9, 12 )

+ 3 +3 +3 +3

Sequences

What would these sequences look like if we graphed them?

A line?

Possibly, but we need to check

it out! GeoGebra will help us.

Sequences

Sequences

Yes, this is a linear sequence!

How would we find the equation

of the line without graphing?

y = m x + b

Common

difference = 1

Common

difference = 3

Slope= change y = 3

change x 1

y = 3 x + ?

y = 3 x + 1

Sequences

Number Sequences

Term

1

2

3

4

5

6

200

4

Value

?

7

7

10

13

16

19

22

What is the 7th term of this sequence?

What is the 200th term of this sequence?

Sequences

Slide Courtesy of Guy Barmoha

Number Sequences

Term

1

2

3

4

5

6

200

4

Value

?

7

7

10

13

16

19

22

22

What is the 7th term of this sequence?

What is the 200th term of this sequence?

seq_line2.ggb

Sequences

Sequences

Term

1

2

3

4

5

6

4

Value

To find the nth term algebraically, use

an = a1 + (n-1) d

a1 = initial term, d = common difference

.

7

200

7

10

13

16

19

22

?

What equation is this?

Slope-Intercept Form

y = 3x + 1

y = 3(200) + 1

y = 601

Sequences

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]

Sequences

Sequences: Segments in GeoGebra

Slide 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.

Sequences

seq_line_art1.ggb

Segment Sequences

Markus’

line art tool

seq_line_art2.ggb

Sequences

Sequences of Segments on a Circle

seq_circle_segments1.ggb

seq_circle_segments3.ggb

Sequences

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 joan.carter@browardschools.com
• Special thanks to Dr. Markus Hohenwarter
• and Guy Barmoha, MST.

Sequences