2.1 Inductive reasoning, conjectures, and counterexamples

Front

What is inductive reasoning?

Back

Inductive reasoning is a method of reasoning in which a general conclusion is drawn from specific examples or patterns.

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What is a conjecture?

Back

A conjecture is a statement believed to be true based on observations, but not yet proven.

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What is a counterexample?

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A counterexample is an example that disproves a conjecture or statement.

Front

Find the next number in the sequence: 5, -10, 15, -20, ________

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25

Front

Make a conjecture about the next item in the sequence: 12, 6, 3, 1.5, 0.75, . . . . .

Back

Divide the previous number by 2.

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What are the missing numbers in this pattern? 23, 33, ___, 53, ___, 73

Back

43, 63

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What are the next two numbers in this pattern? 12, 17, 22, 27, ___, ___

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32, 37

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How do you identify a pattern in a sequence?

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To identify a pattern, look for a consistent relationship between the numbers, such as addition, subtraction, multiplication, or division.

Front

What is the difference between a conjecture and a theorem?

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A conjecture is an unproven statement based on observations, while a theorem is a statement that has been proven based on previously established statements.

Front

Provide an example of a conjecture.

Back

If a number is even, then it is divisible by 2.