1. Find a pattern for each sequence. Use the pattern to show the next 2 terms. 5, 10, 20, 40, … 1, 2, 6, 24, 120, … 1, 3, 7, 13, 21, … M, V, E, M, … 80, 160 720, 5040 31, 43 J, S

2. What did you just do?

3. 1-1 Patterns and Inductive Reasoning LEQ: How do you use inductive reasoning to make conjectures?

4. What is inductive reasoning? Reasoning that is based on patterns you observe. U

5. Example: Finding and using a pattern. Use the pattern to show the next 2 terms in the sequence. 3, 6, 12, 24, … 48 96

6. 1, 2, 4, 7, 11, 16, 22, … 29 37

7. Monday, Tuesday, Wednesday,… Thursday Friday

8. What is a conjecture? A conclusion you reach using inductive reasoning.

9. Example: Using Inductive Reasoning. Make a conjecture about the sum of the first 30 odd numbers. Find the first few sums. Notice that each sum is a perfect square. 1 = 1 = 1 + 3 = 4 = 1 +3 + 5 = 9 = Using inductive reasoning you can conclude that the sum of the first 30 odd numbers is 30 squared, or 900.

10. What is a counterexample? An example for which the conjecture is false. You can prove that a conjecture is false by finding one counterexample.

11. Example: Testing a conjecture and finding a counterexample. If it is cloudy, then it is raining. It is cloudy and it is not raining.

13. Writing Prompt: Explain how you would use inductive reasoning to create a conjecture.

14. Homework: Pgs. 6 – 7 #s 2 – 46 even.