What defines an arithmetic sequence?

• A. A sequence where the ratio between terms is constant
• B. A sequence of numbers whose sum is constant
• C. A sequence where the difference between consecutive terms is constant
• D. A sequence of prime numbers

Answer: (C)

An arithmetic sequence is defined by a consistent difference between consecutive terms. In such a sequence, you take the previous term and add a fixed number, known as the common difference, to arrive at the next term. For instance, in the sequence 3, 7, 11, 15, the common difference is 4—each term is obtained by adding 4 to the previous term.

This characteristic allows for a predictable pattern and straightforward calculations, such as finding the nth term or summing the terms of the sequence. The other choices do not accurately describe an arithmetic sequence; for example, the first option describes a geometric sequence, where the ratio between terms is constant. The second option discusses a constant sum, but that concept does not apply to arithmetic sequences as they can have variable sums depending on how many terms are included. Lastly, a sequence of prime numbers does not have a consistent difference between its elements, as primes are defined by their own properties unrelated to arithmetic sequences.