1. Find a pattern for each sequence
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
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
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 = = 4 = = 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.

12. If the day of the week is Monday, I will be in a bad mood.
This Monday is Labor Day, which means that there is no school, which means that I will most definitely be in a good mood.

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

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