'successively served' is correct and usable in written English
It can be used when describing something that was done or experienced in a series or sequence. For example, "He successively served in the army, navy, and air force."
At Tepco, from 1959 to 2010, four former top-ranking ministry officials successively served as vice presidents at the company.
During her many years with the American Museum of Natural History in New York City, she successively served as assistant curator (1926 42), associate curator (1942 64), curator of ethnology (1964 69), and curator emeritus (1969 78).
Following Cnut's death Stigand successively served Cnut's sons, Harold Harefoot (reigned 1035 1040) and Harthacnut (reigned 1040 1042).
In January , 1958 he began to work at the Institute of Microbiology and Epidemiology, Academy of Military Medical Sciences, successively serving as a research assistant, assistant professor, associate professor and professor.
He served successively at the Universities of Zurich, Prague, and Berlin, at the Kaiser Wilhelm Institute, and at the Prussian Academy of Sciences.
The Kent-Delord House (1797) served successively as British and American headquarters and is maintained as a museum.
During Fianna Fáil's years out of government, Cowen served successively as opposition spokesperson for agriculture, food, and forestry (1994 97) and for health (1997).
After Itō became prime minister in 1885, Inoue served successively as foreign minister, minister of the interior, and minister of finance.
In his youth Frederick served successively as bishop coadjutor (i.e., assistant bishop with the right of succession) of the German dioceses of Bremen, Verden, and Halberstadt.
While there, he served successively as director of the psychological laboratory (1894 1901), professor and head of the psychology department (1905 19), dean of faculties (1911 19), and acting president (1918 19).
He then entered politics, was elected to the Congress, and served successively as minister of public instruction, of justice, and of the interior.
