This is an arithmetic sequence where the first few terms are 8, 14, 20, and 26. In an arithmetic sequence, the difference between consecutive terms is constant, which is called the "common difference."

Step 1: Identify the common difference

The difference between each consecutive term is:

• $14 - 8 = 6$
• $20 - 14 = 6$
• $26 - 20 = 6$

So, the common difference $d$ is 6.

Step 2: General formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \cdot d$ where:

• $a_n$ is the nth term,
• $a_1$ is the first term (which is 8 in this case),
• $d$ is the common difference (6), and
• $n$ is the position of the term in the sequence.

Step 3: Substitute the values

Substitute $a_1 = 8$ and $d = 6$ into the formula: $a_n = 8 + (n - 1) \cdot 6$ Simplify the expression: $a_n = 8 + 6n - 6$ $a_n = 6n + 2$

Conclusion

The nth term rule for the sequence is: $a_n = 6n + 2$

Would you like more details or have any questions?

Here are 5 related questions you could explore:

1. What is the 10th term of this arithmetic sequence?
2. How can you find the sum of the first 20 terms of this sequence?
3. How do you derive the formula for the nth term in an arithmetic sequence?
4. Can an arithmetic sequence have a negative common difference? What would it look like?
5. How does changing the first term or common difference affect the sequence?

Tip: In any arithmetic sequence, once you identify the common difference, the nth term formula is straightforward to derive!