This is an arithmetic sequence where the first five terms are:

$4, 9, 14, 19, 24$

Step-by-Step Solution:

Step 1: Identify the first term and the common difference

• The first term $a_1$ of the sequence is 4.
• The common difference $d$ is the difference between consecutive terms:

$d = 9 - 4 = 5$

Step 2: Use the formula for the $n$-th term of an arithmetic sequence

The general formula for the $n$-th term $a_n$ of an arithmetic sequence is:

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

Substitute $a_1 = 4$ and $d = 5$:

$a_n = 4 + (n - 1) \cdot 5$

Simplify:

$a_n = 4 + 5n - 5$ $a_n = 5n - 1$

Final Answer:

The expression for the $n$-th term of this sequence is:

$a_n = 5n - 1$

Would you like more details or have any questions?

Here are five related questions:

1. What is the 10th term of this arithmetic sequence?
2. How do you find the sum of the first $n$ terms of an arithmetic sequence?
3. Can the 100th term of this sequence be negative?
4. How can you verify if a given term belongs to this sequence?
5. How do you derive the formula for the sum of an arithmetic series?

Tip: In an arithmetic sequence, the common difference between consecutive terms remains constant, making it easy to predict future terms.