It seems like you're working with a sequence. From what you've written, it appears that the sequence starts as:

$a_1 = -17, a_2 = -8, a_3 = 1, a_4 = 10$

The formula for the general term seems to follow a recurrence relation:

$a_n = a_{n-1} + \text{something}$

To identify the pattern or recurrence, let's calculate the differences between consecutive terms:

• $a_2 - a_1 = -8 - (-17) = 9$
• $a_3 - a_2 = 1 - (-8) = 9$
• $a_4 - a_3 = 10 - 1 = 9$

It looks like the difference between consecutive terms is consistently 9, which suggests that the sequence is an arithmetic progression with a common difference of 9.

The general form for an arithmetic sequence is:

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

where:

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

Given that $a_1 = -17$ and the common difference $d = 9$, we can write the formula for $a_n$ as:

$a_n = -17 + (n - 1) \cdot 9$

Let me know if you'd like to explore this further or if there's anything else you'd like to clarify!

Further questions for exploration:

1. What are the next 3 terms in this sequence?
2. How would the sequence change if the common difference was negative?
3. How can you solve for a specific term, say $a_7$, using the general formula?
4. Can this formula be applied to sequences that don't have a constant difference?
5. What would happen to the sequence if the first term was changed to 0?

Tip: Always check the differences between consecutive terms first when trying to identify an arithmetic sequence!