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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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slide1
Sequences in GeoGebra

Sequences

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
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

slide4

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

sequences5
Sequences

Sequences

arithmetic 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 sequences7
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

slide9

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

slide11

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

slide12

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

slide13

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

slide14

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

slide15

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

slide16

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

slide17

Segment Sequences

Markus’

line art tool

seq_line_art2.ggb

Sequences

slide18

Sequences of Segments on a Circle

seq_circle_segments1.ggb

seq_circle_segments3.ggb

Sequences

slide19

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