2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94866We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with the property that the consecutive averages of every sequence with terms in A cannot increase from a value less than x to a value greater than x without taking the value x somewhere in between.13 pagesGeneral Mathematics11B99; 26D15text