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1.1 Patterns and Inductive Reasoning

1.1 Patterns and Inductive Reasoning. Chapter 1 Tools of Geometry. Inductive Reasoning: reasoning based on patterns you observe Conjecture: conclusion you reach using inductive reasoning Counterexample: an example that proves the conjecture wrong. Finding and Using a Pattern.

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1.1 Patterns and Inductive Reasoning

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  1. 1.1 Patterns and Inductive Reasoning Chapter 1 Tools of Geometry

  2. Inductive Reasoning: reasoning based on patterns you observe Conjecture: conclusion you reach using inductive reasoning Counterexample: an example that proves the conjecture wrong

  3. Finding and Using a Pattern Find a pattern for each sequence. Use the pattern to show the next two terms in the sequence. • 3, 6, 12, 24, … b.

  4. Finding and Using a Pattern Write the next two terms in each sequence: a. 1, 2, 4, 7, 11, 16, 22, … b. Monday, Tuesday, Wednesday,…

  5. Using Inductive Reasoning Make a conjecture about the sum of the first 30 odd numbers: 1 = 1 = 12 1 + 3 = 4 = 22 1 + 3 + 5 = 9 = 32 1 + 3 + 5 + 7 = 16 = 42 1 + 3 + 5 + 7 + 9 = 25 = 52 1 + 3 + 5 + 7 + 9 + 11 = 36 = 62 Make a conjecture about the first 35 odd numbers.

  6. Testing a Conjecture Give a counterexample: The product of 5 and any number ends in 5. The sum of two numbers is greater than either number. Look in book at example 4, pg 6

  7. Homework Pg 6 1-30 all

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