https://file.aiquickdraw.com/mathbot/file/1729525688387h1pikd4z.jpg

The image displays a sequence of steps showing a growth pattern of small squares. The question is asking if the number of small squares is increasing linearly and how to explain this.

Let's analyze the pattern:

1. **Step 1**: There are 4 small squares.
2. **Step 2**: There are 6 small squares.
3. **Step 3**: There are 9 small squares.

Now, let's determine if the increase is linear:

- From **Step 1 to Step 2**, the increase is \( 6 - 4 = 2 \) squares.
- From **Step 2 to Step 3**, the increase is \( 9 - 6 = 3 \) squares.

The increase is not constant (it goes from 2 to 3 squares), so the growth is **not linear**. Linear growth means the difference between each step would remain the same, which is not the case here.

This growth follows a quadratic pattern because the number of squares increases by progressively larger amounts. This could be expressed by a quadratic relationship like \( n = x^2 \), where \( x \) is the step number.

Would you like more details or have any other questions?

Here are five related questions:
1. How would you define linear vs. quadratic growth?
2. Can you predict how many squares will appear in Step 4?
3. How would you model this pattern mathematically?
4. What would the total number of squares be after 5 steps?
5. Can you express the number of new squares added at each step as a function?

**Tip**: Recognizing growth patterns can help you understand more complex relationships in mathematics, such as sequences and series.

¿El número de cuadrados pequeños está aumentando linealmente? Explica cómo lo sabes.

Analyze whether the number of small squares in a given pattern increases linearly or follows a quadratic sequence. This math problem helps students in Grades 6-8 understand growth patterns, including the distinction between linear and quadratic relationships.

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