The sequence 4, 9, 13, 18 follows a pattern where each term increases by a constant amount from the previous term. Here's the detailed breakdown:

1. Starting Term: The sequence begins with 4.
2. Common Difference: Each successive term is found by adding 5 to the previous term.

This type of sequence is called an arithmetic sequence because it has a constant difference between terms.

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

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

where:

• $a_1$ is the first term (4 in this case),
• $d$ is the common difference (5 here),
• $n$ is the position of the term in the sequence.

Using this, we can find any term in the sequence.

Would you like further details or help finding more terms in this sequence?

Here are some related questions:

1. How do you find the sum of the first $n$ terms in an arithmetic sequence?
2. How would the sequence change if the common difference were negative?
3. What are the characteristics that define arithmetic sequences?
4. How do you recognize a non-arithmetic sequence?
5. What would the next term after 18 be if the pattern continues?

Tip: To verify a sequence is arithmetic, check that the difference between consecutive terms remains constant.