What is the difference between two terms of an arithmetic sequence called?

The difference between two consecutive terms of an arithmetic sequence is called the common difference.

Understanding Arithmetic Sequences

An arithmetic sequence is a series of numbers where the difference between consecutive terms remains constant. This constant difference is key to identifying and working with arithmetic sequences.

• Definition: A sequence of numbers with a constant difference between consecutive terms.
• Common Difference (d): The constant difference between consecutive terms.

Common Difference Explained

The "common difference" is what defines an arithmetic sequence. It is the value you add (or subtract) to get from one term to the next. From the reference: "The difference between two consecutive terms is a constant called the common difference."

Calculating the Common Difference

To find the common difference, simply subtract any term from the term that follows it.

• Formula: d = a_n+1 - a_n (where a_n+1 and a_n are consecutive terms)

Example

Consider the arithmetic sequence: 2, 5, 8, 11, 14...

1. Subtract the first term from the second term: 5 - 2 = 3
2. Subtract the second term from the third term: 8 - 5 = 3
3. Subtract the third term from the fourth term: 11 - 8 = 3

The common difference (d) is 3.