The formula \( d = a_n - a_{n-1} \) represents the common difference \( d \) in an arithmetic sequence. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

### Example:
Consider the arithmetic sequence \( 3, 7, 11, 15, 19, \dots \).

- Here, \( a_1 = 3 \), \( a_2 = 7 \), \( a_3 = 11 \), \( a_4 = 15 \), and \( a_5 = 19 \).
- The common difference \( d \) is calculated as:

\[
d = a_n - a_{n-1}
\]

Let's compute the difference between each consecutive term:

1. \( d = a_2 - a_1 = 7 - 3 = 4 \)
2. \( d = a_3 - a_2 = 11 - 7 = 4 \)
3. \( d = a_4 - a_3 = 15 - 11 = 4 \)
4. \( d = a_5 - a_4 = 19 - 15 = 4 \)

In this case, the common difference \( d \) is \( 4 \), and it remains the same for each pair of consecutive terms in the sequence.

Would you like more details or have any questions about this concept?

Here are 5 related questions to consider:

1. How do you derive the nth term formula for an arithmetic sequence?
2. What is the sum of the first \( n \) terms in an arithmetic sequence?
3. How can you determine if a given sequence is arithmetic?
4. What happens if the common difference \( d \) is negative?
5. How does an arithmetic sequence differ from a geometric sequence?

**Tip:** The nth term of an arithmetic sequence can be calculated using the formula \( a_n = a_1 + (n-1) \times d \).

Explore how to calculate the common difference in an arithmetic sequence using the formula d = an - an-1. This example demonstrates the core concepts of arithmetic sequences and is ideal for students in Grades 6-8.

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