What describes the sum of the terms of an arithmetic sequence?

• A. Arithmetic series
• B. Linear series
• C. Geometric series
• D. Sequence series

Answer: (A)

The sum of the terms of an arithmetic sequence is accurately described by the term "arithmetic series." An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. When you sum the terms of such a sequence, the result is referred to as an arithmetic series.

An arithmetic series can be calculated using the formula ( S_n = \frac{n}{2} (a + l) ), where ( S_n ) is the sum of the first ( n ) terms, ( a ) is the first term, ( l ) is the last term, and ( n ) is the number of terms. This relationship emphasizes the linearity of both the sequence and the summation process, highlighting the foundational concept of an arithmetic progression.

The other terms do not accurately describe the sum of an arithmetic sequence. A linear series does not specifically refer to the summation of an arithmetic sequence. A geometric series involves terms that are multiplied by a common ratio rather than added with a constant difference. The term "sequence series" is not commonly used in mathematics to refer to any known specific type of series, which further reinforces why "arithmetic series" is the most appropriate descriptor in this context.