1. Arithmetic Sequences

2. An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

3. Which of the following sequences are arithmetic
Which of the following sequences are arithmetic? Identify the common difference.
YES
YES NO NO
YES

4. The common difference is always the difference between any term and the term that proceeds that term.
Common Difference = 5

5. The general form of an ARITHMETIC sequence.
First Term:
Second Term:
Third Term:
Fourth Term:
Fifth Term:
nth Term:

6. Formula for the nth term of an ARITHMETIC sequence.
If we know any three of these we ought to be able to find the fourth.

7. Given:
Find:
IDENTIFY
SOLVE

8. Find: What term number is -169?
Given:
Find: What term number is -169?
IDENTIFY
SOLVE

9. Given:
Find:
What’s the real question?
The Difference
IDENTIFY
SOLVE

10. Given:
Find:
IDENTIFY
SOLVE

11. 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

12. 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

13. 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

14. Vocabulary of Sequences (Universal)

15. Given an arithmetic sequence withx 38 15 NA -3
X = 80

16. Try this one:
1.5 16 x NA
0.5

17. 9 x
633 NA 24
X = 27

18. -6 29 20 NA x

19. 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

20. 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