What is the constant difference between the consecutive terms?

The constant difference between consecutive terms in an arithmetic sequence is called the common difference.

Understanding the Common Difference

The common difference is a fundamental concept in arithmetic sequences. According to our reference material, the common difference is:

• The number added to any one term of an arithmetic sequence that generates the subsequent term.

This means you can find the next term in the sequence by simply adding the common difference to the current term.

Example

Let's look at an example of an arithmetic sequence:

2, 5, 8, 11, 14,...

In this sequence, the common difference is 3. You can verify this by subtracting any term from its subsequent term:

• 5 - 2 = 3
• 8 - 5 = 3
• 11 - 8 = 3
• 14 - 11 = 3

How to find the common difference

To find the common difference (d) in an arithmetic sequence, subtract any term from the term that follows it. Mathematically:

• d = a_n+1 - a_n

Where:

• a_n+1 is the (n+1)^th term in the sequence
• a_n is the n^th term in the sequence.