Number Patterns with Rules

A number pattern is a list of numbers that follows a certain rule. If you can figure out the rule, you can predict what numbers will come next in the sequence!

How to Find the Rule

To find the secret rule of a pattern, follow these easy steps:

1. Look at the first two numbers. Are they getting bigger or smaller?
   • If they get bigger, the rule usually involves adding.
   • If they get smaller, the rule usually involves subtracting.
2. Find the difference. How much did the number change by?
3. Test your rule. Check the next numbers in the list to make sure the rule stays exactly the same.

Examples of Number Patterns

Example 1: Getting Bigger

Look at this pattern: $4, 11, 18, 25, \dots$

• From $4$ to $11$, the number goes up by $7$.
• From $11$ to $18$, the number goes up by $7$.
• The Rule: Add $7$ each time.
• Next number: $25 + 7 = 32$.

Example 2: Getting Smaller

Look at this pattern: $100, 90, 80, \dots$

• From $100$ to $90$, the number goes down by $10$.
• From $90$ to $80$, the number goes down by $10$.
• The Rule: Subtract $10$ each time.
• Next numbers: $70, 60, 50$.

Example 3: Doubling

Look at this pattern: $3, 6, 12, 24, \dots$

• From $3$ to $6$, the number doubles.
• From $6$ to $12$, the number doubles.
• The Rule: Double the number (or multiply by $2$) each time.
• Next number: $24 + 24 = 48$.

Tips for Success

Always check your rule at least twice! Just because a rule works for the first two numbers doesn't mean it is the right rule for the whole pattern. Always test it on the third number to be absolutely sure.