The sequence given is: 2, 5, 8, 11, ...

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

$5 - 2 = 3$,
$8 - 5 = 3$,
$11 - 8 = 3$.

So, the common difference $d = 3$.

For an arithmetic sequence, the general formula for the $n$-th term is:

$U_n = a + (n - 1)d$

Where:

• $a$ is the first term (which is 2),
• $d$ is the common difference (which is 3).

Substituting the values:

$U_n = 2 + (n - 1) \times 3$ $U_n = 2 + 3n - 3$ $U_n = 3n - 1$

Thus, the correct formula for the sequence is $\boxed{3n - 1}$, which corresponds to option a.

Do you want more details or have any further questions?

Here are 5 related questions:

1. How do we identify an arithmetic sequence from a set of numbers?
2. What is the formula for the $n$-th term of a geometric sequence?
3. How can we determine the common difference of an arithmetic sequence?
4. Can the formula for an arithmetic sequence be used for any number of terms?
5. How do we find the sum of an arithmetic sequence?

Tip: The formula for the sum of an arithmetic sequence is $S_n = \frac{n}{2} \times (a + l)$, where $a$ is the first term, $l$ is the last term, and $n$ is the number of terms.