https://file.aiquickdraw.com/mathbot/file/1726030688949lc7jpzqj.jpg

Use the equation *n*2 + *n* = 56 to determine which figure has 56 blocks.

The equation \(n^2 + n = 56\) has two solutions: \(n = -8\) and \(n = 7\). Since the number of blocks must be a positive integer, the valid solution is \(n = 7\).

Now, to determine which figure corresponds to 56 blocks, note that each figure in the sequence adds layers of blocks as \(n\) increases. For \(n = 7\), the figure that follows this pattern should have 56 blocks.

Would you like further details on how this sequence grows? Here are some related questions:

### 5 Related Questions:
1. How is the number of blocks in each figure related to the figure number?
2. How can you derive the formula \(n^2 + n = 56\) from the pattern of blocks?
3. Can you visualize the pattern for figures beyond the third one?
4. What is the next figure in the sequence if \(n = 8\)?
5. How can quadratic equations help model real-world patterns?

### Tip:
When solving quadratic equations, always check if the solution is

Use the equation n^2 + n = 56 to determine which figure has 56 blocks.

Solve the quadratic equation n^2 + n = 56 to determine which figure contains 56 blocks. This math problem explores key algebraic concepts, including solving quadratic equations, and is suitable for students in grades 8-10.

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