The board of adjustment shall consist of five members, a majority of whom shall reside within the county but outside the corporate limits of any city, each to be appointed for a term of five years, excepting that when the board shall first be created one member shall be appointed for a term of five years, one for a term of four years, one for a term of three years, one for a term of two years, and one for a term of one year.  Members shall be removable for cause by the appointing authority upon written charges and after public hearing.  Vacancies shall be filled for the unexpired term of any member whose term becomes vacant.