An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which a_n = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a₁. An arithmetic sequence can also be defined recursively by the formulas a₁ = c, a_n+1 = a_n + d, in which d is again the common difference between consecutive terms, and c is a constant.

The sum of an infinite arithmetic sequence is either ∞, if d > 0, or - ∞, if d < 0.

There are two ways to find the sum of a finite arithmetic sequence. To use the first method, you must know the value of the first term a₁ and the value of the last term a_n. Then, the sum of the first n terms of the arithmetic sequence is S_n = n(). To use the second method, you must know the value of the first term a₁ and the common difference d. Then, the sum of the first n terms of an arithmetic sequence is S_n = na₁ + (dn - d ).