To find the 10th term of an arithmetic sequence where the first term \(a_1 = 32\) and the common difference \(d = -6\), we can use the formula for the \(n\)th term:

\[
a_n = a_1 + (n - 1) \times d
\]

### Step 1: Identify the values
- \(a_1 = 32\)
- \(d = -6\)
- \(n = 10\)

### Step 2: Substitute the values into the formula
\[
a_{10} = 32 + (10 - 1) \times (-6)
\]
\[
a_{10} = 32 + 9 \times (-6)
\]
\[
a_{10} = 32 - 54
\]
\[
a_{10} = -22
\]

### Final Answer
The 10th term of the sequence is \(-22\).

Would you like to explore more on this topic or have any other questions?

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Here are five related questions:

1. What is the 15th term of this sequence?
2. How many terms are needed for the sequence to reach a value below \(-50\)?
3. What is the sum of the first 10 terms of this sequence?
4. How would the sequence change if the common difference was \(-8\) instead of \(-6\)?
5. Can you find the 20th term of the sequence?

**Tip:** When working with negative common differences, remember that the sequence decreases over time.

Learn how to find the 10th term of an arithmetic sequence where the first term is 32 and the common difference is -6. Step-by-step solution provided with calculations using the arithmetic sequence nth term formula. Suitable for Grades 7-9 students.

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