Sequence Rules Worksheet

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📚 Part 1: Finding the Pattern

Instructions: Look at each sequence carefully. Work out what is being added or subtracted each time to get from one term to the next. This is called the common difference.

1. Find the next two terms in this sequence: 3, 7, 11, 15, _____, _____

Working: 7 - 3 = _____ , 11 - 7 = _____ , 15 - 11 = _____

The common difference is: _____

2. Find the next two terms: 20, 17, 14, 11, _____, _____

Working: 17 - 20 = _____ , 14 - 17 = _____ , 11 - 14 = _____

The common difference is: _____

3. Find the next two terms: 5, 12, 19, 26, _____, _____

4. Find the next two terms: 100, 95, 90, 85, _____, _____

5. Find the next two terms: 2, 9, 16, 23, _____, _____

🔢 Part 2: Writing Sequence Rules

Instructions: A sequence rule tells us how to get from one term to the next. For example: "Start with 4, then add 3 each time" gives us 4, 7, 10, 13...

6. Write the rule for this sequence: 6, 11, 16, 21, 26

Start with _____ , then _____ _____ each time.

7. Write the rule for this sequence: 50, 45, 40, 35, 30

Start with _____ , then _____ _____ each time.

8. Use the rule "Start with 8, add 5 each time" to write the first 5 terms:

_____ , _____ , _____ , _____ , _____

9. Use the rule "Start with 30, subtract 4 each time" to write the first 5 terms:

_____ , _____ , _____ , _____ , _____

10. Create your own sequence with the rule "Start with 1, add 6 each time":