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The problem involves a pattern where the number of squares increases with each step. The pattern is:

- Step 1: 1 square
- Step 2: 5 squares
- Step 3: 9 squares

The task is to write an equation that represents the number of squares, \( p \), in step \( n \).

Observing the number of squares in each step:
- Step 1: \( p = 1 \)
- Step 2: \( p = 5 \)
- Step 3: \( p = 9 \)

This suggests that the number of squares follows a linear pattern. The given equation \( p = 4n + 1 \) fits the pattern because:

- For \( n = 1 \), \( p = 4(1) + 1 = 5 \).
- For \( n = 2 \), \( p = 4(2) + 1 = 9 \).
- For \( n = 3 \), \( p = 4(3) + 1 = 13 \).

The equation \( p = 4n + 1 \) successfully models the number of squares in step \( n \).

Would you like more details on how this equation is derived, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. How would the equation change if each step had 2 additional squares instead of 4?
2. Can you derive a similar equation for a different pattern?
3. What would the equation look like if the number of squares doubled in each step?
4. How can you use this equation to predict the number of squares in step 10?
5. How does recognizing patterns help in solving real-world problems?

**Tip:** Always check your equation by plugging in values from earlier steps to verify its correctness.

Write an equation that represents the number of squares, p, in step n of the pattern. Step 1 has 1 square, Step 2 has 5 squares, and Step 3 has 9 squares.

Learn how to write an algebraic equation that represents the number of squares, p, in step n of a pattern. This problem involves recognizing a pattern and using the formula p = 4n + 1. Suitable for Grade 6-8 students.

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