1. 12.2 – Arithmetic Sequences and Series

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 NA -3
X = 80

7. Try this one:
1.5 16 x NA
0.5

8. 9 x
633 NA 24
X = 27

9. -6 29 20 NA x

10. Find two arithmetic means between –4 and 5
-4, ____, ____, 5 -4 5 4 NA 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 NA 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. Find n for the series in which5 y x
440 3
Graph on positive window
X = 16

13. -19
353 ?? 63 x 6