The initial board of each district shall divide its members by lot into three classes of as nearly equal size as possible. The terms of the directors in the first, second, and third classes expire on dates of the annual meetings in the first, second, and third years, respectively, following the year in which the district is organized, or as soon thereafter as their successors are elected and have qualified. At the annual meeting in each year after the year in which the district is organized, a director must be elected to succeed each director whose term of office expires on that date, and each director so elected holds office for a term of three years and until a successor is elected and has qualified. Vacancies must be filled for the unexpired term by appointment by the remaining directors.