2. MONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAY DEC 3 UNIT 4 TEST DEC 4 Sequences & Series DEC 5 Sequences & Series DEC 6 Post Test in Computer Lab DEC 7 Sequences & Series DEC 10 Unit 5 Review DEC 11 UNIT 5 TEST DEC 12 EXAM REVIEW DEC 13 EXAM REVIEW DEC 14 REVIEW 1 st Period Final Exam DEC 17 EARLY RELEASE 4 th / 2 nd Exam DEC 18 EARLY RELEASE 5 th / 3 rd Exam DEC 19 EARLY RELEASE 6 th / 7 th Exam

3. Sequences and Series (Purple Book 4.7 – 4.9) Tuesday Dec 4 th, Wednesday Dec 5 th, Friday Dec 6 th

4. 4.7 Sequences

5. Vocabulary Sequence: an ordered list of numbers –Ex: 3, 2, 1, 0, -1, -2 Term: each number in a sequence –Ex: a 1, a 2, a 3, a 4, a 5, a 6 Infinite Sequence: sequence that continues infinitely –Ex: 2, 4, 6, 8, … Finite Sequence: sequence that ends –Ex: 2, 4, 6 Explicit Formula: defines the nth term of a sequence.

6. Example 1: A)Write the first six terms of the sequence defined by a n = 4n + 5

7. Example 1: B.Write the first six terms of the sequence defined by a n = 2n 2 – 1

8. 4.7 Series

9. Series Series: the sum of a sequence –Sequence: 1, 2, 3, 4 –Series: 1 + 2 + 3 + 4 Summation Notation: Summation Notation - __________________ EX. (for the above series)

10. = _______ + _______ + _______ + _______ = ____ + _____ + _____ + _____ = _____

11. Example 3: A)Evaluate B)Evaluate

12. 4.8 Arithmetic Sequences

13. MONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAY DEC 3 UNIT 4 TEST DEC 4 Sequences & Series DEC 5 Sequences & Series DEC 6 Post Test in Computer Lab DEC 7 Sequences & Series DEC 10 Unit 5 Review DEC 11 UNIT 5 TEST DEC 12 EXAM REVIEW DEC 13 EXAM REVIEW DEC 14 REVIEW 1 st Period Final Exam DEC 17 EARLY RELEASE 4 th / 2 nd Exam DEC 18 EARLY RELEASE 5 th / 3 rd Exam DEC 19 EARLY RELEASE 6 th / 7 th Exam

14. Vocabulary Arithmetic Sequence: –A sequence generated by adding “d” a constant number to pervious term to obtain the next term. –This number is called the common difference. What is d? a 2 – a 1 – 3, 7, 11, 15, …d = 4 – 8, 2, -4, -10, … d = -6

15. Formula for the n th term a n = a 1 + (n – 1)d What term you are looking for First term in the sequence What term you are looking for Common difference

16. Example 1: A)Find the 10 th term of a 1 = 7 and a n = a n-1 + 6 B)Find the 7 th term of a 1 = 2.5 and a n = a n-1 - 3 d

17. Example 2: A)Find the 10 th term of the arithmetic sequence where a 3 = -5 and a 6 = 16

18. B. Find the 15 th term of the arithmetic sequence where a 5 = 7 and a 10 = 22

19. C. Find the 12 th term of the arithmetic sequence where a 3 = 8 and a 7 = 20

20. Arithmetic & Geometric Sequences Friday December 7 th

21. MONDAYTUESDAYWEDNESDAYTHURSDAYFRIDAY DEC 7 Sequences & Series DEC 10 Unit 5 Review DEC 11 UNIT 5 TEST DEC 12 EXAM REVIEW DEC 13 EXAM REVIEW DEC 14 REVIEW 1 st Period Final Exam DEC 17 EARLY RELEASE 4 th / 2 nd Exam DEC 18 EARLY RELEASE 5 th / 3 rd Exam DEC 19 EARLY RELEASE 6 th / 7 th Exam

22. 4.8 Arithmetic Series

23. Vocabulary An Arithmetic Series is the sum of an arithmetic sequence. Formula for arithmetic series S n =

25. Example 2: A)Given 3 + 12 + 21 + 30 + …, find S 25 B)Given 16, 12, 8, 4, …, find S 11

26. Example 3: A)Evaluate

27. Example 3: B)Evaluate

28. 4.9 Geometric Sequences

29. Vocabulary Geometric Sequence: –A sequence generated by multiplying a constant ratio to the previous term to obtain the next term. –This number is called the common ratio. What is r?  2, 4, 8, 16, …r = 2  27, 9, 3, 1, …r = 1/3

30. Formula for the n th term a n = a 1 r n-1 What term you are looking for First term in the sequence What term you are looking for Common Ratio

31. Example 1 A) Find the 5 th term of a 1 = 8 and a n = 3a n-1 B) Find the 7 th term of a 1 = 5 and a n = 2a n-1

32. Example 2: A)Find a 10 of the geometric sequence 12, 18, 27, 40.5, … B)Find a 7 of the geometric sequence where a 1 = 6 and r = 4

33. 4.9 Geometric Series

34. Vocabulary An Geometric Series is the sum of an geometric sequence. Formula for geometric series S n =

35. Example 1: Given the series 3 + 4.5 + 6.75 + 10.125 + …find S 10 to the nearest tenth.

36. Example 2: Evaluate n a1a1 r

37. Example 2: Evaluate n a1a1 r