Find the general term of the sequence 8,14,20,26,..

The sequence given is \(8, 14, 20, 26, \dots\).

### Step 1: Identify the Pattern
Let's first identify the pattern or the common difference. Notice how each term in the sequence is obtained by adding 6 to the previous term:
- \( 14 - 8 = 6 \)
- \( 20 - 14 = 6 \)
- \( 26 - 20 = 6 \)

The common difference (\(d\)) is \(6\).

### 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, \(a_1 = 8\) and \(d = 6\).

Substituting these into the formula:
\[
a_n = 8 + (n - 1) \times 6
\]
\[
a_n = 8 + 6n - 6
\]
\[
a_n = 6n + 2
\]

### Final Answer
The general term of the sequence is:
\[
a_n = 6n + 2
\]

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

Here are some related questions you might be interested in:

1. What is the 15th term of this sequence?
2. How can you find the sum of the first \(n\) terms of this sequence?
3. How do you determine if a specific number belongs to this sequence?
4. Can you find the 50th 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 10 terms of this sequence?
8. How does changing the first term affect the sequence?

**Tip:** When working with arithmetic sequences, always check if the sequence can be easily described using a common difference. This helps simplify finding any term in the sequence.

Learn how to find the general term of the sequence 8, 14, 20, 26, ... using the formula for arithmetic sequences. This problem involves identifying the common difference and applying the general term formula. Suitable for Grades 7-9.

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