-4,-6,-8,...10th term            an=a1+(n-1)d

To find the 10th term of the arithmetic sequence \(-4, -6, -8, \dots\), we'll use the formula for the \(n\)th term of an arithmetic sequence:

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

### Step 1: Identify the first term (\(a_1\)) and the common difference (\(d\))
- The first term, \(a_1\), is \(-4\).
- The common difference, \(d\), is found by subtracting the first term from the second term:

\[
d = -6 - (-4) = -6 + 4 = -2
\]

### Step 2: Apply the formula to find the 10th term (\(a_{10}\))
Substitute \(a_1 = -4\), \(d = -2\), and \(n = 10\) into the formula:

\[
a_{10} = -4 + (10 - 1) \cdot (-2)
\]

\[
a_{10} = -4 + 9 \cdot (-2)
\]

\[
a_{10} = -4 - 18
\]

\[
a_{10} = -22
\]

So, the 10th term of the sequence is \(-22\).

Would you like more details or have any questions?

### Related Questions:
1. What is the general formula for the \(n\)th term of any arithmetic sequence?
2. How do you find the common difference if you're given any two terms in a sequence?
3. What is the sum of the first 10 terms of this sequence?
4. How can you determine if a sequence is arithmetic or geometric?
5. Can an arithmetic sequence have a positive common difference?

**Tip:** The common difference in an arithmetic sequence can be positive or negative, affecting whether the sequence increases or decreases.

Discover how to find the 10th term of the arithmetic sequence -4, -6, -8, ... using the formula for the nth term of an arithmetic sequence. This problem covers key concepts such as arithmetic sequences, nth term formula, and common difference calculation. Suitable for high school students.

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