find the general term of the sequence 38,34,30,26,...

The sequence given is \(38, 34, 30, 26, \dots\).

### Step 1: Identify the Pattern
To determine the general term, let's first identify the pattern or the common difference. Notice how each term in the sequence is obtained by subtracting 4 from the previous term:
- \( 34 - 38 = -4 \)
- \( 30 - 34 = -4 \)
- \( 26 - 30 = -4 \)

The common difference (\(d\)) is \(-4\).

### Step 2: Use the Arithmetic Sequence Formula
For an arithmetic sequence, the general term (\(a_n\)) can be expressed as:
\[
a_n = a_1 + (n - 1) \times d
\]
where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

### Step 3: Substitute the Values
Here, \(a_1 = 38\) and \(d = -4\).

Substituting these into the formula:
\[
a_n = 38 + (n - 1) \times (-4)
\]
\[
a_n = 38 - 4(n - 1)
\]
\[
a_n = 38 - 4n + 4
\]
\[
a_n = 42 - 4n
\]

### Final Answer
The general term of the sequence is:
\[
a_n = 42 - 4n
\]

Would you like any further details or have any other questions? 

Here are some related questions you might be interested in:

1. How can you determine the sum of the first \(n\) terms of this sequence?
2. What is the 10th term of this sequence?
3. How do you determine if a specific number belongs to this sequence?
4. Can you find the 100th term of the sequence?
5. What is the arithmetic mean of the first 5 terms of the sequence?
6. How can this sequence be represented graphically?
7. What is the sum of the first 20 terms of this sequence?
8. How does changing the common difference affect the sequence?

**Tip:** In an arithmetic sequence, the common difference is always constant, which means the difference between any two consecutive terms is the same throughout the sequence.

Learn how to find the general term of the sequence 38, 34, 30, 26, ... with a detailed step-by-step solution. This problem involves identifying the arithmetic sequence pattern and using the arithmetic sequence general term formula. Suitable for high school students.

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