4.8 Writing Equations from Patterns A very useful problem-solving strategy is look for a pattern. When you make a conclusion based on a pattern of examples,

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4.8 Writing Equations from Patterns A very useful problem-solving strategy is look for a pattern. When you make a conclusion based on a pattern of examples, you are using inductive reasoning. Recall that deductive reasoning uses facts, rules, or definitions to reach a conclusion.

Extend a Pattern Example 1 p. 240.

Patterns in a Sequence Find the next three terms in the sequence 3, 6, 12, 24, … You can use inductive reasoning to find the next term in a sequence. Notice the pattern 3, 6, 12, … The difference between each term doubles in each successive term. To find the next three terms in the sequence, continue doubling each successive difference. Add 24, 48, and 96. The next three terms are 48, 96, and 192.

Write Equations Sometimes a pattern can lead to a general rule. If the relationship between the domain and range of a relation is linear, the relationship can be described by a linear equation.

Write an Equation from Data Example 3 p. 242.