In an arithmetic sequence, what is the "common difference"?

In an arithmetic sequence, each term is generated by adding a fixed value to the previous term. This fixed value is known as the "common difference." It is the amount by which each term increases or decreases to obtain the next term. For instance, in the sequence 2, 5, 8, 11, the common difference is 3, as 5 - 2 = 3 and 8 - 5 = 3.

This concept is fundamental to understanding the structure of an arithmetic sequence, as it directly influences the progression of the terms. Without the common difference, the sequence would not maintain its defining linear pattern, which is crucial to its identification as arithmetic. Each other answer choice does not encapsulate this key aspect of the arithmetic sequence clearly. The initial term refers to the starting value of the sequence, the ratio between terms pertains to geometric sequences, and the average of the first and last terms does not define any characteristic of the sequence's progression. Therefore, recognizing the common difference as the value that separates consecutive terms is essential to grasp the nature of arithmetic sequences.