Resumen: We give two extensions of the classical formula for sums of powers on arithmetic progressions. This is achieved by using an identity involving binomial mixtures, which can be viewed as a generalization of the binomial transform. Idioma: Inglés DOI: 10.1186/s13662-017-1250-y Año: 2017 Publicado en: Advances in Difference Equations 2017, 1 (2017), [5 pp] ISSN: 1687-1839 Factor impacto JCR: 1.066 (2017) Categ. JCR: MATHEMATICS rank: 57 / 309 = 0.184 (2017) - Q1 - T1 Categ. JCR: MATHEMATICS, APPLIED rank: 106 / 252 = 0.421 (2017) - Q2 - T2 Factor impacto SCIMAGO: 0.539 - Algebra and Number Theory (Q2) - Applied Mathematics (Q2) - Analysis (Q3)