FIND A PATTERN FOR EACH SEQUENCE. USE THE PATTERN TO SHOW THE NEXT 2 TERMS.

1. 5, 10, 20, 40, …

2. 1, 2, 6, 24, 120, …

3. 1, 3, 7, 13, 21, …

4. M, V, E, M, …

80, 160

720, 5040

31, 43

J, S

WHAT DID YOU JUST DO?

1-1 PATTERNS AND INDUCTIVE REASONINGLEQ: How do you use inductive reasoning to make conjectures?

WHAT IS INDUCTIVE REASONING?

Reasoning that is based on patterns you observe.

U

EXAMPLE: FINDING AND USING A PATTERN. USE THE PATTERN TO SHOW THE NEXT 2 TERMS IN THE SEQUENCE.

3, 6, 12, 24, …

48

96

1, 2, 4, 7, 11, 16, 22, …

29

37

Monday, Tuesday, Wednesday,…

Thursday

Friday

WHAT IS A CONJECTURE?

A conclusion you reach 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 =

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.

WHAT IS A COUNTEREXAMPLE?

An example for which the conjecture is false.

You can prove that a conjecture is false by finding one counterexample.

EXAMPLE: TESTING A CONJECTURE AND FINDING A COUNTEREXAMPLE.

If it is cloudy, then it is raining.

It is cloudy and it is not raining.

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.

WRITING PROMPT:

Explain how you would use inductive reasoning to create a conjecture.

HOMEWORK:

Pgs. 6 – 7 #s 2 – 46 even.