Alexander Sloan earned a bachelor of science degree from the University of Maryland in 1955. He attended West Virginia Medical School from 1955 to 1957, then transferred to the University of Pennsylvania Medical School, where he earned a doctor of medicine degree in 1959. He was commissioned as an Air Force Medical Officer in 1960, and from 1991 to 1994 he served as the 14th Surgeon General of the Air Force. He retired in 1994 as a U.S. Air Force Lieutenant General.