https://file.aiquickdraw.com/mathbot/file/1726399253911pqvx413f.jpg

The image shows a pattern of blue dots arranged in three stages, labeled as 1, 2, and 3. To write a term representing the pattern mathematically, we need to identify the rule behind the number and arrangement of dots at each stage.

- **Stage 1** has 2 dots.
- **Stage 2** has 4 dots.
- **Stage 3** has 6 dots.

It looks like the number of dots is increasing by 2 in each step. We can assume that the number of dots in each stage follows a simple arithmetic sequence. Specifically, the number of dots seems to follow the formula:

\[
a_n = 2n
\]

Where \( a_n \) represents the number of dots at stage \( n \). This formula suggests that at each stage \( n \), there are \( 2n \) dots.

Would you like a detailed explanation of how I derived the formula or any additional clarifications?

Here are 5 related questions to further your understanding:
1. What is the general form of an arithmetic sequence?
2. How can you find the next stage of this pattern using the formula?
3. How would you modify the term if the difference between stages increased differently?
4. What happens if the pattern starts from a different initial number of dots?
5. Can you represent this pattern graphically, and what would it look like?

**Tip:** When working with arithmetic sequences, always identify the common difference between terms to establish a clear formula.

Explore how to write a term for a pattern using arithmetic sequences, with a practical example of increasing dot patterns. Suitable for middle school students learning about simple sequences and their formulas.

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