How do you find the common difference in an arithmetic sequence worksheet?

To find the common difference in an arithmetic sequence, you simply subtract any term from the term that immediately follows it.

Finding the Common Difference (d)

The common difference, often denoted as d, is the constant value added to each term in an arithmetic sequence to get the next term. Here's how to find it:

• Identify two consecutive terms: Pick any two terms next to each other in the sequence. Let's call the first term you picked a_1 and the term immediately following it a_2.

• Subtract: Subtract the first term (a_1) from the second term (a_2). The result is the common difference (d).

  d = a_2 - a_1

Example

According to the reference: In the arithmetic sequence 3, 9, 15, 21, 27, 33,...

1. Let a_1 = 3 and a_2 = 9.
2. Then d = 9 - 3 = 6.

Therefore, the common difference is 6. You can verify this by checking other consecutive terms. For instance, 15-9 = 6, and 21-15 = 6.

Summary

Step	Description	Formula
1	Identify two consecutive terms.	a_1, a_2
2	Subtract the first term from the second term.	d = a_2 - a_1