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Patterns and Sequences sol 6.17 by k woodard and k norman

Patterns and Sequences sol 6.17 by k woodard and k norman. Arithmetic Sequence. Add or Subtract the same number each time This is called the common difference examples 2, 4, 6, 8, … common difference is + 2 1600, 1500, 1400, 1300, … common difference is -100.

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Patterns and Sequences sol 6.17 by k woodard and k norman

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  1. Patterns and Sequencessol 6.17 by k woodardand k norman

  2. Arithmetic Sequence • Add or Subtract the same number each time This is called the common difference examples • 2, 4, 6, 8, … common difference is + 2 • 1600, 1500, 1400, 1300, … common difference is -100

  3. Arithmetic Sequences • 4, 7, 10, 13,… • Common difference: + 3 • 27, 24, 21, 18,… • Common difference: -3 • 5, 20, 35, 50,… • Common difference: + 15

  4. Arithmetic Sequences areLinear Patterns Line ar When you graph the pattern it makes a line It goes up or down gradually.

  5. Geometric Sequence • Multiply or Divide by the same number each time This is called the common ratio examples • 1, 4, 16, 64, … common ratio is x 4 • 400, 200, 100, 50, … common ratio is 2

  6. Geometric Sequence • 4, 8, 16, 32, 64, 128,… • Common ratio: x 2 • 2000, 1000, 500, 250, 125, 62.5,… • Common ratio: 2 • 6, 24, 96, 384, 1536, 6144,… • Common ratio: x 4

  7. Geometric Sequences areExponential Patterns ial Exponent When you graph the pattern it makes a steep curve It goes up or down fast!

  8. Make your own patterns Geometric Arithmetic • Start at 1, rule: x 2 • Start at 1000, /2 • Start at 3, x 3 • Start at 390,625, /5 • Start at 218,700, /3 • Start at 1, x 4 • Start at 1, rule: +2 • Start at 1000, -50 • Start at 12, +6 • Start at 81, -9 • Start at 13, +5 • Start at 20, -4

  9. 08 SOL 6.17*

  10. 08 SOL 6.17*

  11. 06 SOL 6.17

  12. Powers of 10 • Ten to the 3rd power • =10 x 10 x 10 = 1000 exponent base

  13. Powers of Base 10

  14. 08 SOL

  15. 08 SOL 6.21, 6.22*

  16. Look for patterns all around you

  17. Square Numbers • Numbers that can be represented by dots in a square array. • 1st four square numbers are depicted below:

  18. Floor Tiles = 1 = 4 = 9 = 16 = 25 Perfect Square Numbers!

  19. Triangular Numbers • Numbers that can be represented by dots in a triangular array. • 1st four triangular numbers are depicted below: 1 3 6 10 +2 +3 +4

  20. http://collegian.csufresno.edu/2008/04/18/chingy-for-change-a-cause-on-pause-for-a-quick-game/http://collegian.csufresno.edu/2008/04/18/chingy-for-change-a-cause-on-pause-for-a-quick-game/ 1 , 3 , 6 , 10

  21. 07 SOl

  22. 08 SOL

  23. 06 SOL

  24. 07 SOL

  25. Fibonacci Sequence http://www.fibonacci.name/

  26. Fibonacci Sequence

  27. 1+1 =2 1+2 =3 2+3 =5 3+5 =8 5+8 =13 mat-cast.com

  28. Fibonacci Sequence

  29. Perfect Square Multiply n*n 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 The Fab 5 Arithmetic + or – the common difference 2, 4, 6, 8, 10 Triangular Add one more each time 1, 3, 6, 10 Geometric X or / the common ratio 2, 4, 8, 16, 32 1, 10, 100, 1000 Fibonacci Add the last 2 to get the next 1, 1, 2, 3, 5, 8, 13, 21, 34 worksheet

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