An introduction…………

1. Unit 5 – Series, Sequences, and LimitsSection 5.1 – Arithmetic and Geometric SequencesCalculator Required

2. Arithmetic Series Geometric Series Sum of Terms Sum of Terms An introduction………… Geometric Sequences Arithmetic Sequences ADD To get next term MULTIPLY To get next term

3. Find the next four terms of –9, -2, 5, … Arithmetic Sequence 7 is referred to as the common difference (d) Common Difference (d) – what we ADD to get next term Next four terms……12, 19, 26, 33

4. Find the next four terms of 0, 7, 14, … Arithmetic Sequence, d = 7 21, 28, 35, 42 Find the next four terms of x, 2x, 3x, … Arithmetic Sequence, d = x 4x, 5x, 6x, 7x Find the next four terms of 5k, -k, -7k, … Arithmetic Sequence, d = -6k -13k, -19k, -25k, -32k

5. Vocabulary of Sequences (Universal)

6. Given an arithmetic sequence with x 38 15 -3 X = 80

7. 1.5 x 16 0.5 Try this one:

8. 9 633 x 24 X = 27

9. -6 20 29 x

10. The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence Find two arithmetic means between –4 and 5 -4, ____, ____, 5 -4 5 4 x

11. The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence Find three arithmetic means between 1 and 4 1, ____, ____, ____, 4 1 4 5 x

12. Vocabulary of Sequences (Geometric)

13. Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

14. 1/2 x 9 2/3

15. The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 x

16. -3, ____, ____, ____

17. x 9

18. x 5

19. *** Insert one geometric mean between ¼ and 4*** 1/4 3