🔍 Part 1: Pattern Recognition

1. Look at this growing pattern: 2, 5, 8, 11, 14, ...

What is the constant difference between terms? _______

What would be the next two terms? _______, _______

2. Complete the table for the pattern: 3, 6, 9, 12, ...

3. Which of these represents a growing pattern?

1, 4, 2, 8, 3, 12, ...

5, 10, 15, 20, 25, ...

2, 4, 2, 4, 2, 4, ...

10, 8, 6, 4, 2, ...

4. Draw or describe the 4th term in this shape pattern:

Term 1: 1 square, Term 2: 3 squares, Term 3: 5 squares

📝 Part 2: Algebraic Rules

5. For the pattern 4, 8, 12, 16, 20, ... write the algebraic rule.

If n represents the position number, the rule is: _______________

6. Using your rule from question 5, predict these terms:

10th term: _______

20th term: _______

50th term: _______

7. Match each pattern with its correct algebraic rule:

Pattern: 1, 3, 5, 7, ...

Pattern: 2, 4, 6, 8, ...

Pattern: 5, 10, 15, 20, ...

Rule: 5n

Rule: 2n

Rule: 2n - 1

8. Create your own growing pattern and write its rule:

My pattern: _______, _______, _______, _______, _______

My rule: _______________

🎯 Part 3: Reasoning and Justification

9. Explain how you would find the 100th term in the pattern 7, 14, 21, 28, ... without writing out all the terms.

10. A student says the rule for 1, 4, 7, 10, ... is "add 3 each time." Another student says the rule is "3n - 2." Are both students correct? Explain your thinking.

Algebraic Patterns Exploration

Algebraic Patterns Exploration

🔍 Part 1: Pattern Recognition

📝 Part 2: Algebraic Rules

🎯 Part 3: Reasoning and Justification

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