Sequences

Math 4MM4A9: 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.

• With a recursive formula, the previous term in the sequence is used to generate the next term

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 – { }

Examples 1-4

Assignment

• Pg. 696, 11-35 odd

Do Now

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

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}

Assignment

• Pg. 696, 10-34 even

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}

Assignment

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

Pg. 975, 11.1, 1-6 / Worksheet pg. 68, 1-6

1. {5, 2, -1, -4, -7}2. {-8, -4, 0, 4, 8}3. {2, 8, 18, 32, 50}4. {1, 6, 11, 16, 21}5. {16, 10, 4, -2, -8}6. {3, 6, 12, 24, 48}

1. {2.5, 5, 7.5, 10, 12.5, 15}

2. {0, ½, 1, 3/2, 2, 5/2}3. {13, 16, 21, 28, 37, 48}4. {20, 70, 220, 670, 2020,

6070}5. {1, 101, 201, 301, 401,

501}6. {-5, -15, -45, -135,

-405, -1215}

11.1 Continued

• Summation Properties and Formulas• EQ: How do I evaluate the sum of a series

expressed in sigma notation?

Summation Properties

1. To define the summation of a one term expression multiply the coefficient by the summation of the variable.

2. To find the summation of an expression that contains more than one term, find the summation of each individual term.

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.

Examples

Assignment

• Pg 696, #’s 42-50 all

Do Now: Solve

52

1

3k

x

Pg. 696, 42-50 all

42. 1243. 4044. 3045. 2446. -3047. -50

48. 749. 55/350. -100/3

Assignment

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

Pg. 975, 11.1, 10-15/wkbk pg. 68, 13-20

10. 25811. 3012. 13013. 10514. 13515. 34

13. 12614. 18515. 21016. -2417. 1018. 1432.519. 39720. 1911.4

Pg. 696-697, 51-74 all

• Omit # 71 and # 72

Pg. 696-697, 51-74 all (omit 71-72)

51. 5/252. 3253. -1554. 15455. 2356. 5257. 1258. 859. 8460. 84

61. 42 73. 6862. 32 74. 64563. 3964. 16565. 16466. -11467. 668. 19969. -88/2170. 698/15