The given sequence is:

$\{10, 14, 18, 22, 26, \dots\}$

This is an arithmetic sequence, where the common difference ($d$) between consecutive terms is:

$d = 14 - 10 = 4$

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

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

Here, the first term ($a_1$) is 10, and $d = 4$. Substituting these values into the formula:

$a_n = 10 + (n-1)(4)$

Simplify the expression:

$a_n = 10 + 4n - 4$ $a_n = 4n + 6$

Final Answer:

$a_n = 4n + 6$

Let me know if you would like further clarification or more examples!

Here are some related questions you might find helpful:

1. What is the 10th term of this sequence?
2. How would the formula change if the common difference was 6 instead of 4?
3. Can you derive the sum of the first $n$ terms of this sequence?
4. How can this formula be verified for any term of the sequence?
5. How does the formula for an arithmetic sequence differ from that of a geometric sequence?

Tip: Always verify your formula by plugging in small values of $n$ to ensure it matches the given terms of the sequence.