Pattern rules specify how a sequence or set of paired values is generated, such as adding or subtracting a constant amount, multiplying by a constant factor, or applying a simple operation to an input to obtain an output. The learner interprets lists, tables, and coordinate graphs to explain relationships, distinguish a term-to-term rule from a rule based on position or input, and predict missing or later values; formal functions and generalized algebraic rules beyond these familiar cases are not included.
A pattern rule tells how numbers in a pattern are made. Look for what changes from one number to the next.
Worked example
Find the rule for this pattern and find the value at position .
| Position | ||||
|---|---|---|---|---|
| Value |
Step 1: Compare neighboring values.
The pattern adds each time.
So the term-to-term rule is:
Add to get the next value.
Step 2: Continue the pattern.
The next value is
The value after that is
So the value at position is .
Step 3: Describe the rule using the position.
The value is also times the position, plus :
This is a position rule. It tells how to find any value directly. For position :
Both rules describe the same pattern: the term-to-term rule says add each time, while the position rule says multiply the position by , then add .
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?