1 / 19

Sequences in GeoGebra

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.

sasha-ruiz
Download Presentation

Sequences in GeoGebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Sequences in GeoGebra Sequences Sequences

  2. 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

  3. 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

  4. 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

  5. Sequences Sequences

  6. 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

  7. 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

  8. What would these sequences look like if we graphed them? Sequences

  9. 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

  10. What would these sequences look like if we graphed them? seq_line1.ggb Sequences

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. Segment Sequences Markus’ line art tool seq_line_art2.ggb Sequences

  18. Sequences of Segments on a Circle seq_circle_segments1.ggb seq_circle_segments3.ggb Sequences

  19. 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

More Related