The question asks for an explicit formula for the sequence $9, 7, 5, \dots$. This is an arithmetic sequence, where the difference between consecutive terms is constant.

First, we identify the common difference:

• The difference between 9 and 7 is $7 - 9 = -2$,
• The difference between 7 and 5 is $5 - 7 = -2$.

So, the common difference $d = -2$.

In an arithmetic sequence, the general formula for the $n$-th term is given by: $a_n = a_1 + (n - 1) d$ where:

• $a_1 = 9$ (the first term),
• $d = -2$ (the common difference).

Substituting these values into the formula: $a_n = 9 + (n - 1)(-2)$ Simplifying the equation: $a_n = 9 - 2(n - 1) = 9 - 2n + 2 = 11 - 2n$

Looking at the answer choices:

• $a_n = 9 - 2(n - 1)$ simplifies to $11 - 2n$, which matches one of the choices.

Therefore, the correct option is the formula $a_n = 9 - 2(n - 1)$.

Would you like further clarification on this, or to explore other aspects of the problem? Here are some related questions:

1. How do you derive the formula for an arithmetic sequence in general?
2. What are the key differences between arithmetic and geometric sequences?
3. How can you identify whether a sequence is arithmetic by just looking at a few terms?
4. Can you explain the significance of the common difference in arithmetic sequences?
5. How would the formula change if the first term of the sequence were different?

Tip: For arithmetic sequences, knowing the first term and the common difference allows you to generate any term in the sequence with ease!