"Quasquicentennial" is the official term used to describe a 125th anniversary. The word is pronounced kwos-kwi-sen-ten-ee-uhl and is a combination of quasqui, which means "one and a quarter," and centennial, which refers to a period of 100 years.
Frank W. Hatten contacted Funk and Wagnalls in 1961 seeking an appropriate term for a 125th anniversary. After testing out a few different ideas, Dr. Wilford Funk decided upon the word quasquicentennial, though the adjective did not become popular until several years later. In 1965, a scholar named Robert Chapman discussed the history of this unique term in an issue of American Speech. As of 2014, the word is still listed in the dictionary.