We observe that Faulhaber’s theorem on sums of odd powers holds an random arithmetic progression, the odd power sums of any arithmetic progression: a+b, a+2b,…, a+nb is a polynomial in n a + n(n+1)b/2. This assertion can be presumed from the original Faulhaber’s theorem. We use the Bernoulli polynomials for the alternative formula. By using the central factorial numbers as in the approach of knuth, we can derive the formulas for r – fold sums of powers without restoring the notion of r – reflective functions. We can also provide formulas for the r-fold alternating sums of powers in terms of Euler polynomials. In its simplest case, a power sum is a sum of the form Sn(l) = 1n + 2n + . . . . . +(l-1)n Their sums have interesting combination of a number theoretical importance, and were already known by Bernoulli’s, but we shall see that even today there are many things about them to discover. • Basics of power sums • Generalizations of power sums • Alternating power sums In this paper, we are going to discuss about the negative power sum.