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 $a_n = a_1 + (n-1) \times d$.