1-1 Patterns and Inductive Reasoning

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Presentation transcript:

1-1 Patterns and Inductive Reasoning

What do you know? Pretest

Inductive Reasoning is based on patterns we observe. Find the pattern and the next two terms in each sequence: 5, 10, 15, 20, _____, _____

You try these: 2, 4, 8, 16, ____, ____ 4, 44, 444, 4444, ______, ______ 1, -2, 3, -4, ____, ____ 100, 50, 25, 12.5, ____, ____ O, T, T, F, F, S, S, ____, ____

A conjecture is a conclusion reached by inductive reasoning. Let’s make a conjecture about the sum of the first 30 odd numbers. 1 1+3 1+3+5 1+3+5+7 1+3+5+7+9 The sum of the first 30 odd numbers is ______. The sum of the first n odd numbers is ______.

Conjecture Examples

A counterexample is an example for which the conjecture is incorrect. Give a counterexample to the statements: “All numbers are positive.” “All animals have four legs”

Find a counterexample: The sum of two numbers is greater than either number. The product of two positive numbers is greater than either number.

Exit Slip Homework