The given sequence is:

$9, 7, 5, \ldots$

This sequence is decreasing by 2 each time, which suggests it's an arithmetic sequence where the common difference $d = -2$.

The general formula for the $n$-th term of an arithmetic sequence is:

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

Where:

• $a_n$ is the $n$-th term,
• $a_1$ is the first term,
• $d$ is the common difference.

For the given sequence:

• $a_1 = 9$,
• $d = -2$.

Now substitute these values into the formula:

$a_n = 9 + (n - 1) \cdot (-2)$

Simplify:

$a_n = 9 - 2(n - 1)$ $a_n = 9 - 2n + 2$ $a_n = 11 - 2n$

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

$\boxed{a_n = 11 - 2n}$

Would you like further explanation, or do you have any questions?

Here are 5 related questions:

1. What is the 10th term of this sequence?
2. How would the formula change if the common difference were $-3$?
3. Can you derive the sum of the first $n$ terms of this sequence?
4. How do you identify an arithmetic sequence in general?
5. What is the common difference in a sequence like 15, 12, 9, 6, ...?

Tip: Arithmetic sequences are linear, meaning their graph forms a straight line!