At the election, the names of up to three candidates for trustee shall be written in by the voters on blank ballots without formal nomination and the board shall appoint three from among the five receiving the highest number of votes as trustees for the district. One trustee shall be appointed to serve for one year, one for two years, and one for three years. The trustees and their successors must be residents of the district and shall give bond in the amount required by the board, the premium of which shall be paid by the district. Vacancies shall be filled by election, but if there are no candidates for a trustee office, the vacancy may be filled by appointment by the board. The term of succeeding trustees shall be three years.