The members of the district board in office on September 15, 1961, shall, as soon as practicable thereafter, so classify themselves, by lot, that a majority of the members serve until January 1, 1963, and a minority of the members of the district board shall serve until January 1, 1965, or until the appointment of their successors or their resignation or termination of residence within the area they represent. Thereafter, the term of office of each succeeding member of the district board shall be four years and each shall hold office until the appointment of his or her successor or his or her resignation or termination of residence within the area he or she represents.