1. Unit 5 – Series, Sequences, and Limits Section 5
Unit 5 – Series, Sequences, and Limits Section 5.1 – Arithmetic and Geometric Sequences Calculator Required

2. An introduction…………
Arithmetic Series
Sum of Terms
Geometric Series
Sum of Terms
Arithmetic Sequences
Geometric 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 withx 38 15 -3
X = 80

7. Try this one:
1.5 16 x
0.5

8. 9 x
633 24
X = 27

9. -6 29 20 x

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

11. Find three arithmetic means between 1 and 4
1, ____, ____, ____, 4 1 4 5 x
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

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

16. -3, ____, ____, ____

17. x 9

18. x 5

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