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!