1. 4.2 Using Inductive Reasoning

2. 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.

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

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

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

6. 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 =

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

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

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

10. Assignment