1. Chapter 5: Graphs & Functions 5.7 Describing Number Patterns

2. Inductive Reasoning Making conclusions based on patterns you observe Conjecture: – Conclusion you reach by inductive reasoning

3. Example 1 Use inductive reasoning to describe each pattern, then find the next two numbers in the pattern: 2, 5, 8, 11, … 2, 4, 8, 16, … 1, 4, 9, 16, …

4. Example 1a Use inductive reasoning to describe each pattern, then find the next two numbers in the pattern: 3, 9, 27, 81, … 9, 15, 21, 27, … 2, -4, 8, -16, …

5. Sequences – Number patterns Term – Each number in a sequence Arithmetic sequence – Adds a fixed number to each previous term Common difference – Number added to the previous term

6. Example 2 Find the common difference of each arithmetic sequence: -7, -3, 1, 5, … 17, 13, 9, 5, …

7. Example 2a Find the common difference of each arithmetic sequence: 11, 23, 35, 47, … 8, 3, -2, -7, …

8. Arithmetic Sequence Nth term First term Term number Common difference

9. Example 3 Find the tenth term of the sequence that has a first term 32, and a common difference of -2.

10. Example 3a Find the first, sixth, and twelfth terms of each sequence:

11. Example 3a Find the first, sixth, and twelfth terms of each sequence:

12. Homework P. 294 2-42 even, 56, 58