The given sequence is: $-1, 2, 5, 8, 11$

This appears to be an arithmetic sequence, where each term increases by a constant difference. Let's calculate the common difference:

$2 - (-1) = 3$ $5 - 2 = 3$ $8 - 5 = 3$ $11 - 8 = 3$

So, the common difference $d = 3$.

The general form for the $n$-th term of an arithmetic sequence is given by:

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

Where:

• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

For this sequence:

• $a_1 = -1$,
• $d = 3$.

Substituting these values into the formula:

$a_n = -1 + (n-1) \cdot 3$ $a_n = -1 + 3n - 3$ $a_n = 3n - 4$

Thus, the $n$-th term of the sequence is:

$a_n = 3n - 4$

Would you like further details on this, or do you have any questions?

Here are 5 questions related to arithmetic sequences:

1. How do you find the sum of the first $n$ terms of an arithmetic sequence?
2. How does the formula for the $n$-th term change if the common difference is negative?
3. Can you apply this formula to find the 10th term of the sequence?
4. What is the general condition for a sequence to be arithmetic?
5. How would you find the common difference if the terms were given as algebraic expressions?

Tip: In arithmetic sequences, the difference between consecutive terms is always constant. This can help quickly identify such sequences.