https://file.aiquickdraw.com/mathbot/file/17333413963256v4asmm0.jpg

Please extend the pattern until figure 13

To extend the pattern to Figure 13, we need to analyze the progression of figures in the image:

### Observations:
1. **Figure 1:** Contains \(2 \times 2 = 4\) squares, with one additional square space at the bottom right.
2. **Figure 2:** Contains \(3 \times 3 = 9\) squares, with one additional row and column added compared to Figure 1, and an additional square space at the bottom right.
3. **Figure 3:** Contains \(4 \times 4 = 16\) squares, with one more row and column added, and the same additional square space.

### Pattern:
Each subsequent figure adds one row and one column, forming a square grid. An additional row and column space are left at the bottom right.

#### General Formula for \(n\)-th Figure:
- Total grid squares (without spaces): \(n \times n\)
- Additional row/column spaces: 1.

#### Figure 13:
For Figure 13:
- Total grid squares = \(13 \times 13 = 169\).
- The bottom-right corner will have an extra space for one row and one column.

Would you like me to provide a diagrammatic representation or more detailed visualization of this? 

### Related Questions:
1. How can we generalize this pattern mathematically for any figure \(n\)?
2. What is the total number of empty spaces created up to Figure 13?
3. How does the perimeter of the square evolve as the figure progresses?
4. What real-world applications could such patterns relate to?
5. Can this pattern be extended into three dimensions? 

**Tip:** Look for patterns in row or column growth to simplify calculations in geometric sequences

Learn how to extend a growing square pattern to Figure 13 with detailed calculations. Explore the arithmetic and geometric growth concepts, including formulas for square numbers and additional spaces. Suitable for Grades 6-8 students.

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