1. Arithmetic Sequences

2. Identifying if a sequence is arithmetic:
The sequence must have a common difference if it is arithmetic. Just having a pattern is not enough.

3. Examples:
5, 7, 9, 11…
2, -4, -10, -15…
2, 4, 8, 16…
1, 4, 9, 16…
8, 5, 2, -1…
Identify if the sequence if arithmetic or not. If so state the first term and the common difference.

4. If we determine that it is arithmetic, then there are multiple ways to represent it.

5. If a sequence if Arithmetic then it is also linear
If a sequence if Arithmetic then it is also linear. The common difference is the slope. The “zero” term is the y-intercept. We can use this information to write the equation in slope-intercept form which is also called Function form. This is one of three ways to represent the sequence in equation form.

6. There are three types of equations that you can write.
Explicit
Recursive
Function Form

7. Recursive Form:
a formula used to find the next term of a sequence when the previous term is known

8. Recursive Form:
Lists the first term and uses the common difference to show how to get to the next term.

9. Practice – Determine if arithmetic. If so, Write the Recursive formula
5, 10,15,20…
1,2,4,8…
12, 9, 6, 3…
8,12,16,20…

10. Explicit Rule
The explicit rule is used to find any term in the sequence not just the next one

11. Explicit Rule for Arithmetic Sequences

12. Practice – Determine if arithmetic. If so, Write the explicit formula
5, 10,15, 20…
1, 2 ,4, 8…
12, 9, 6, 3…
8, 12, 16, 20…

13. To create the function Rule, use the “zero” term as the y-intercept and the common difference as the slope

14. Practice – Determine if arithmetic. If so, Write the Function formula
5, 10,15,20…
1,2,4,8…
12, 9, 6, 3…
8,12,16,20…