At the election, the names of candidates for trustee shall be written in by the voters on blank ballots without formal nomination, and the board of supervisors shall appoint three from among the five receiving the highest number of votes as trustees for the district; one 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 which the board of supervisors may require, the premium of which shall be paid by the district the trustees represent. Vacancies may thereafter be filled by election, or by appointment by the board of supervisors. The term of succeeding trustees shall be for three years.