The given sequence is $18, 9, 0, -9$.

First, let's determine if this is an arithmetic sequence. An arithmetic sequence has a common difference $d$ between consecutive terms.

To find the common difference $d$: $d = 9 - 18 = -9$ $d = 0 - 9 = -9$ $d = -9 - 0 = -9$

The common difference $d$ is $-9$, so this is an arithmetic sequence.

Next, the general formula for the $n$-th term of an arithmetic sequence is given by: $a_n = a + (n-1)d$

Where:

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

Given $a = 18$ and $d = -9$, we want to find the $n$-th term, $a_n$.

The general formula becomes: $a_n = 18 + (n-1)(-9)$

Simplify the expression: $a_n = 18 - 9(n-1)$ $a_n = 18 - 9n + 9$ $a_n = 27 - 9n$

This is the formula for the $n$-th term of the sequence. If you need a specific term, you can substitute $n$ into this formula.

If you have any further questions or need details on a specific term calculation, please let me know!

Would you like the details on how this formula was derived, or have any other questions? Here are 8 related questions to expand your understanding:

1. What is the 5th term of the sequence?
2. How do you determine if a sequence is arithmetic or geometric?
3. What is the sum of the first 10 terms of this arithmetic sequence?
4. How can we find the 100th term of the sequence?
5. What is the common difference of the sequence?
6. How do we derive the formula for the $n$-th term of an arithmetic sequence?
7. What happens if the common difference is positive?
8. How does the common difference affect the growth or decay of the sequence?

Tip: When dealing with sequences, identifying whether they are arithmetic (constant difference) or geometric (constant ratio) is crucial for using the appropriate formulas.