In a statutory strong-mayor-council city, there shall be a personnel board consisting of three members elected by the council for staggered six-year terms. The council shall elect the three original members so that the term of one member will expire in each succeeding even-numbered year. The term of their successors shall be for six (6) years, beginning at 7:30 o'clock p.m. on the first Monday in May in every even-numbered year. Members shall serve until their successors are elected and qualified, and they shall serve without compensation unless the council provides otherwise. The council, by a vote of a majority of its members, after adequate opportunity for a public hearing, may remove a member for the good of the service, and may fill vacancies for the unexpired term.