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Sequences

Sequences. Math 4 MM4A9: Students will use sequences and series. EQ. How do I find the terms of a sequence using explicit and recursive formulas?. Formulas. With an explicit formula , the number of the term is used to generate the terms of the sequence.

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Sequences

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  1. Sequences Math 4 MM4A9: Students will use sequences and series

  2. EQ • How do I find the terms of a sequence using explicit and recursive formulas?

  3. Formulas • With an explicit formula, the number of the term is used to generate the terms of the sequence. • With a recursive formula, the previous term in the sequence is used to generate the next term

  4. Vocabulary • Sequence – an ordered list of numbers • Term – a number in a sequence *A sequence can be infinite (never ending) or finite. *Answers must be in brackets – { }

  5. Examples 1-4

  6. Assignment • Pg. 696, 11-35 odd

  7. Do Now • Pg. 696, #’s 36-37 • Keep your answers in fraction form

  8. Pg. 696, 11-35 odd 11. {5, 9, 13, 17} 13. {-5, -9, -13, -17} 15. {4, 9, 14, 19} 17. {4, 0, -4, -8} 19. {3/2, 2, 5/2, 3} 21. {12.42, 21.17, 29.92, 38.67} 23. {1, 8, 27, 64} 25. {-2, -8, -18, -32} 27. {2, 4, 6, 8, 10, 12} 29. {-6, 15, -27, 57, -111, 225} 31. {10; 51; 256; 1281; 6,406; 32,031} 33. {8, 22, 64, 190, 568, 1702} 35. {3.34, 6.348, 12.9656, 27.52432, 59.553504, 130.0177088}

  9. Assignment • Pg. 696, 10-34 even

  10. Pg. 696, 10-34 even 10. {5, 7, 9, 11} 12. {-1, -3, -5, -7} 14. {8, 14, 20, 26} 16. {-4, -11, -18, -25} 18. {6, 10, 14, 18} 20. {9/4, 5/2, 11/4, 3} 22. {6.26, 10.02, 13.78, 17.54} 24. {-1, 1, -1, 1} 26. {1, 4, 7, 10, 13, 16} 28. {0, -4, -8, -12, -16, -20} 30. {7, 29, 117, 469, 1877, 7509} 32. {10, 31, 94, 283, 850, 2551} 34. {-2.24, -0.488, 1.6144, 4.13728, 7.164736, 10.7976832}

  11. Assignment • Pg. 975, 11.1, 1-6 • Worksheet, 11.1, 1-6

  12. Pg. 975, 11.1, 1-6 / Worksheet pg. 68, 1-6 • {5, 2, -1, -4, -7} • {-8, -4, 0, 4, 8} • {2, 8, 18, 32, 50} • {1, 6, 11, 16, 21} • {16, 10, 4, -2, -8} • {3, 6, 12, 24, 48} • {2.5, 5, 7.5, 10, 12.5, 15} • {0, ½, 1, 3/2, 2, 5/2} • {13, 16, 21, 28, 37, 48} • {20, 70, 220, 670, 2020, 6070} • {1, 101, 201, 301, 401, 501} • {-5, -15, -45, -135, -405, -1215}

  13. 11.1 Continued • Summation Properties and Formulas • EQ: How do I evaluate the sum of a series expressed in sigma notation?

  14. Summation Properties • To define the summation of a one term expression multiply the coefficient by the summation of the variable. • To find the summation of an expression that contains more than one term, find the summation of each individual term.

  15. Summation Formulas • Identify the value of “n”, which is the top number in the sigma notation. • To find the summation for a constant series, multiply “n” by the constant. • To find the summation for a linear series, multiply “n” by (n+1) and divide by 2. • To find the summation for a quadratic series, multiply “n” by (n+1) and by (2n+1) and divide by 6.

  16. Examples

  17. Assignment • Pg 696, #’s 42-50 all

  18. Do Now: Solve

  19. Pg. 696, 42-50 all 42. 12 43. 40 44. 30 45. 24 46. -30 47. -50 48. 7 49. 55/3 50. -100/3

  20. Assignment • Pg. 975, 11.1 10-15 • Worksheet, 11.1, 13-20

  21. Pg. 975, 11.1, 10-15/wkbk pg. 68, 13-20 • 258 • 30 • 130 • 105 • 135 • 34 13. 126 14. 185 15. 210 16. -24 17. 10 18. 1432.5 19. 397 20. 1911.4

  22. Pg. 696-697, 51-74 all • Omit # 71 and # 72

  23. Pg. 696-697, 51-74 all (omit 71-72) 51. 5/2 52. 32 53. -15 54. 154 55. 23 56. 52 57. 12 58. 8 59. 84 60. 84 61. 42 73. 68 62. 32 74. 645 63. 39 64. 165 65. 164 66. -114 67. 6 68. 199 69. -88/21 70. 698/15

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