It looks like you're working with a sequence defined by the equation:

\[
a_n = 3n - 2
\]

This equation defines the \(n\)th term of a sequence. Let's analyze it:

### Understanding the Sequence

- **General Form:** The \(n\)th term of the sequence \(a_n\) is given by \(a_n = 3n - 2\).
- **Type of Sequence:** This is an arithmetic sequence, where each term is a linear function of \(n\). 

### Finding Specific Terms

You can find the first few terms of the sequence by substituting \(n = 1, 2, 3, \dots\) into the equation.

1. **For \( n = 1 \):**
   \[
   a_1 = 3(1) - 2 = 3 - 2 = 1
   \]
2. **For \( n = 2 \):**
   \[
   a_2 = 3(2) - 2 = 6 - 2 = 4
   \]
3. **For \( n = 3 \):**
   \[
   a_3 = 3(3) - 2 = 9 - 2 = 7
   \]
4. **For \( n = 4 \):**
   \[
   a_4 = 3(4) - 2 = 12 - 2 = 10
   \]

### Pattern and Formula
The sequence progresses as 1, 4, 7, 10, and so on. This sequence increases by 3 each time, which is consistent with the arithmetic sequence defined by the common difference of 3.

### Summary

- **General Formula:** \(a_n = 3n - 2\)
- **First few terms:** 1, 4, 7, 10, ...

Would you like further details on this sequence, or do you have any other questions?

Here are 5 related questions you might find useful:

1. What is the 10th term of the sequence defined by \(a_n = 3n - 2\)?
2. How would the sequence change if the formula was \(a_n = 4n - 3\)?
3. Can you find the sum of the first 5 terms of this sequence?
4. What is the common difference in the sequence \(a_n = 3n - 2\)?
5. How would you find the \(n\)th term if the formula was \(a_n = 5n + 1\)?

**Tip:** In an arithmetic sequence, the difference between consecutive terms is constant, which is a key characteristic that helps in identifying and working with such sequences.

Explore the arithmetic sequence defined by the equation a_n = 3n - 2. Learn how to find specific terms, identify the pattern, and derive the general formula. Suitable for Grades 7-9.

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