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Sequences

Sequences. 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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Sequences

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  1. Sequences 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

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