At the annual meeting of any cemetery district next following the annexation of territory under the provisions of this act*, a majority of the electors present shall have authority to determine the number of and to elect not less than five nor more than nine directors who shall hold their office until the next annual meeting of the electors of such district. Directors shall reside either (1) in the county or counties in which such cemetery district is located or (2) within 25 miles of the cemetery district boundaries. Upon the change of residency of any director as required by this section, such director’s office shall be deemed to be vacated, and a successor shall be appointed to serve the remainder of the unexpired term by the remaining directors.