Chapter 5: Graphs & Functions 5.7 Describing Number Patterns.

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Chapter 5: Graphs & Functions 5.7 Describing Number Patterns

Inductive Reasoning Making conclusions based on patterns you observe Conjecture: – Conclusion you reach by inductive reasoning

Example 1 Use inductive reasoning to describe each pattern, then find the next two numbers in the pattern: 2, 5, 8, 11, … 2, 4, 8, 16, … 1, 4, 9, 16, …

Example 1a Use inductive reasoning to describe each pattern, then find the next two numbers in the pattern: 3, 9, 27, 81, … 9, 15, 21, 27, … 2, -4, 8, -16, …

Sequences – Number patterns Term – Each number in a sequence Arithmetic sequence – Adds a fixed number to each previous term Common difference – Number added to the previous term

Example 2 Find the common difference of each arithmetic sequence: -7, -3, 1, 5, … 17, 13, 9, 5, …

Example 2a Find the common difference of each arithmetic sequence: 11, 23, 35, 47, … 8, 3, -2, -7, …

Arithmetic Sequence Nth term First term Term number Common difference

Example 3 Find the tenth term of the sequence that has a first term 32, and a common difference of -2.

Example 3a Find the first, sixth, and twelfth terms of each sequence:

Example 3a Find the first, sixth, and twelfth terms of each sequence:

Homework P even, 56, 58