1.1 Patterns and Inductive Reasoning
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11 Patterns and Inductive Reasoning
ObjectiveUse inductive reasoning to make conjectures.
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IncorrectCorrect
Which do you think describes the square of any odd number?
It is odd.
HOW DO YOU KNOW?
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Reasoning based on patterns that you observe is calledINDUCTIVE REASONING.
Find a pattern for this sequence. Find the next two terms in the sequence.
3 6 12 24...
48 96
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A conclusion you reach using inductive reasoning is called aCONJECTURE.
Make a conjecture about the sum of the first 30 odd numbers.
Step 1: Find the first few sums.
1 = 1 + 3 =1 + 3 + 5 =1 + 3 + 5 + 7 =
Step 2: Find a pattern.
1 = 1 = 12 1 + 3 = 4 = 221 + 3 + 5 = 9 = 321 + 3 + 5 + 7 = 16 = 42
Step 3: Make a conclusion.
The sum of the first 30odd numbers is302 or 900.
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Not all conjectures turn out to be true!
You can prove that a conjecture is false byfinding one COUNTEREXAMPLE.
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Find a counterexample that makes these conjectures false:
The square of any number is greater than the original number.
Any number and its absolute value are opposites.
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HOMEWORK
p. 6 # 16, 1718, 1922, 2526, 51, 52CHALLENGE #54