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.