Identify the Rule in a Number Pattern

How to identify the rule in a number pattern

A number pattern is a list of numbers that follows a rule. Your job is to figure out what changes from one term to the next and describe that change clearly.

1. Look for a repeated change

Compare consecutive terms:

• Add or subtract the same number each time? Then the rule is a constant difference.
• Multiply or divide by the same number each time? Then the rule is a constant ratio.
• If the changes are not constant, look for a repeating structure or a pattern in the differences.

2. Write the rule in words

State the pattern simply, such as:

• “Add 3 each time”
• “Subtract 2 each time”
• “Multiply by 4 each time”

If the exercise asks for an exact answer, keep the rule precise and simplify any arithmetic you use.

3. Test your rule

Apply your rule to one or two terms and check whether it produces the next numbers in the sequence. A correct rule should match every term given.

4. Watch for common mistakes

Do not focus on only one pair of numbers. Check the whole sequence, because a rule must work for all the terms shown.

Quick check

If you can generate the next term from the previous one using your rule, you likely identified the pattern correctly.