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To determine if the sequence \(13, 20, 27, 34, \dots\) is arithmetic, we need to check if there is a constant difference between consecutive terms.

Let's calculate the differences:

1. \(20 - 13 = 7\)
2. \(27 - 20 = 7\)
3. \(34 - 27 = 7\)

Since the difference between consecutive terms is consistently \(7\), the sequence is arithmetic, and the common difference is \(7\).

Thus, the correct answer is:
- **a. yes; 7**

Would you like more details or have any further questions?

Here are five related questions to expand on this topic:
1. What is the general formula for the nth term of an arithmetic sequence?
2. How can we find the sum of the first \(n\) terms in an arithmetic sequence?
3. Can a sequence be geometric if the difference between terms is constant?
4. How would the sequence change if the common difference were negative?
5. What are some real-life examples of arithmetic sequences?

**Tip:** When analyzing sequences, always calculate the difference between consecutive terms to check if it's arithmetic.

Is the sequence arithmetic? If so, identify the common difference. 13, 20, 27, 34, ...

Learn how to determine if the sequence 13, 20, 27, 34, ... is arithmetic and identify the common difference. This step-by-step solution covers key concepts of arithmetic sequences and how to calculate the common difference. Suitable for students in Grades 6-8.

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