4.2 Using Inductive Reasoning

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Presentation transcript:

4.2 Using Inductive Reasoning

A _________________ is an unproven statement that is based on observations. You use ________________________ when you find a pattern in specific cases and then write a conjecture for the general case. A _______________ is a specific case for which a conjecture is false.

Example 1 Study the figures below. Describe how to sketch the fourth figure in the pattern. Then, sketch the fourth figure.

Example 2 Describe the pattern in the numbers -1, -4, -16, -64 . . . and write the next three numbers in the pattern.

You try Describe the pattern in the numbers 1, 3, 9, 27, 81 . . . and write the next three numbers in the pattern.

Example 3 Numbers such as 1, 3, and 5 are called consecutive odd numbers. Make a conjecture about the sum of any three consecutive odd numbers. Hint: Start by finding 1 + 3 + 5 =

What conjecture can be made from Example 3? Can you test your conjecture further?

Example IV Find a counterexample to show that the conjecture is false. Conjecture: All even numbers are composite numbers. Counterexample:

You Try Find a counterexample to show the conjecture is false. Conjecture: The product of two fractions is a fraction. Counterexample:

Assignment