The governing body of the authority shall be a board consisting of seven members, two of whom shall, ex officio, be the mayor of the city requesting the establishment of the authority and the chairman of the board of county commissioners wherein the authority is located. Each of these ex officio members shall serve without bond during their respective terms as mayor and chairman. The remaining five members shall be residents of the county in which the authority is located. Two of these members shall be originally appointed for a term of two years and three for a term of four years from the date of their appointment, and thereafter the members shall hold office for a term of four years and until their successors are appointed and have qualified. The Governor, in making the original appointments, shall designate the term of each appointee. Any vacancy, in the appointed members of the board for any reason, shall be filled for the unexpired term by an appointment by the Governor. No appointive member shall hold office for more than three successive full terms. Each appointive member, before entering upon the duties of his office, shall file with the Secretary of State an oath that he will duly and faithfully perform to the best of his ability all duties of his office, as provided in sections 14-1701 to 14-1725, and a bond in the penal sum of five thousand dollars executed by one or more qualified sureties for the faithful performance of all his duties as a member of the board of such authority. If any appointive member fails to file such oath and bond with the Secretary of State within thirty days after written notice of such appointment, the office shall be deemed to be vacant and a new appointment made.