The given equation is \( a_1 = 3n^2 - 2 \).

To interpret this equation, it typically describes a sequence where each term \( a_1 \) depends on \( n \), which is the term number. In this case, the first term of the sequence \( a_1 \) is given by the formula \( 3n^2 - 2 \).

If we need to find the value of \( a_1 \) for different values of \( n \), we substitute \( n \) into the formula. 

Let's compute the first few terms of the sequence:

1. For \( n = 1 \):
   \[
   a_1 = 3(1)^2 - 2 = 3 \cdot 1 - 2 = 1
   \]

2. For \( n = 2 \):
   \[
   a_1 = 3(2)^2 - 2 = 3 \cdot 4 - 2 = 12 - 2 = 10
   \]

3. For \( n = 3 \):
   \[
   a_1 = 3(3)^2 - 2 = 3 \cdot 9 - 2 = 27 - 2 = 25
   \]

4. For \( n = 4 \):
   \[
   a_1 = 3(4)^2 - 2 = 3 \cdot 16 - 2 = 48 - 2 = 46
   \]

So, the first few terms of the sequence are \( 1, 10, 25, 46 \).

Would you like more details on this sequence, or do you have any specific questions?

Here are some related questions to expand on this information:

1. How do we determine the general term \( a_n \) for different types of sequences?
2. What are the properties of quadratic sequences?
3. How can we find the sum of the first \( n \) terms in a sequence?
4. What is the difference between arithmetic and geometric sequences?
5. How do we find the common difference in an arithmetic sequence?
6. What is the significance of the leading coefficient in a quadratic sequence?
7. How can sequences be applied in real-world scenarios?
8. What methods can be used to find the nth term in more complex sequences?

**Tip:** When working with sequences, always identify the pattern or rule that defines the sequence to easily find any term.

Explore how to interpret and compute terms in a quadratic sequence defined by the formula a₁ = 3n² - 2. Learn to calculate specific terms and understand the pattern of the sequence. Suitable for students in Grades 9-12.

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