This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript m], is expressed in terms of the preceding ones, S[subscript m]?1 , S[subscript m]?2,...., S[subscript 0]. This recurrence, which has been derived previously by methods other than the one used here, is solved explicitly for S[subscript m]. The final result is expressed in the form of a determinant of order (m + 1) by (m + 1). A comparison is made with other methods, including Inaba's recent approach in this journal.