To describe an arithmetic sequence, we use the formula for the $n$-th term:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_n$ is the $n$-th term of the sequence,
• $a_1$ is the first term of the sequence,
• $d$ is the common difference between consecutive terms,
• $n$ is the position of the term in the sequence.

For example, in the sequence $1, 5, 9, 13$:

• $a_1 = 1$ (the first term),
• $d = 4$ (the common difference).

So, the formula for the $n$-th term would be:

$a_n = 1 + (n - 1) \cdot 4$

This can be simplified to:

$a_n = 4n - 3$

Would you like more details or have any questions?

Here are five related questions:

1. How would you use this formula to find the 10th term of the sequence?
2. How do you find the common difference given two terms in an arithmetic sequence?
3. What is the sum of the first 20 terms of this sequence?
4. Can an arithmetic sequence have a negative common difference?
5. How can you derive the formula for the sum of an arithmetic sequence?

Tip: When working with arithmetic sequences, always double-check the common difference to ensure consistency throughout the sequence.