The equation you provided is the formula for the **n-th term** of a **geometric sequence**. Specifically, it is written as:

\[
a_n = a_1 \cdot r^{n-1}
\]

Where:
- \(a_n\) is the n-th term in the sequence,
- \(a_1\) is the first term in the sequence,
- \(r\) is the common ratio (the factor by which each term is multiplied to get the next term),
- \(n\) is the position of the term in the sequence.

This formula allows you to find the value of any term in the geometric sequence if you know the first term \(a_1\), the common ratio \(r\), and the position \(n\).

Would you like to see an example of how to use this formula or go deeper into geometric sequences?

Here are 5 related questions that expand on this concept:
1. How do you find the common ratio \(r\) if you know two terms of a geometric sequence?
2. How do you derive the sum of the first \(n\) terms of a geometric sequence?
3. What happens if the common ratio \(r\) is less than 1 or negative?
4. How do geometric sequences apply to real-life situations like compound interest?
5. How does a geometric sequence differ from an arithmetic sequence?

**Tip:** When the common ratio \(r\) is between 0 and 1, the terms of the sequence decrease and approach zero!

Discover how to find the n-th term in a geometric sequence using the formula aₙ = a₁ * r^(n-1). This explanation covers key algebraic concepts, such as the first term, common ratio, and sequence position. Suitable for students in Grades 9-12.

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