2.1.1 Using Inductive Reasoning to Make Conjectures − Worksheet
Example 1: Find the next item in each pattern. 1. March, May, July, ... 2.
1 3
2 4
3 5
3.
,
,
,
,
,
, …
Example 2: Complete each conjecture. 4. The product of two even numbers is ? .
5. A rule in terms of n for the sum of the first n odd positive integers is ? .
Example 3: 6. A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria increases.
Example 4: Show that each conjecture is false by finding a counterexample. 7. President
Age at Inauguration
Washington T. Roosevelt Truman Kennedy Clinton
57 42 60 43 46
Kennedy is the youngest U.S. president to be inaugurated.
8. Three points on a plane always form a triangle.
9. For any real number x , if x 2 ≥ 1, then x ≥ 1.
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