What is a formula for the nth term of the given sequence?
9, comma, 7, comma, 5, point, point, .
9,7,5...

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!

What is a formula for the nth term of the given sequence? 9,7,5...

Find the formula for the nth term of the arithmetic sequence 9, 7, 5... This problem involves identifying the common difference and applying the arithmetic sequence formula. Suitable for students in Grades 6-8.

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