The members who are first appointed shall be designated to serve for terms of one, two (2), three (3), four (4), and five (5) years respectively. If a legislative body adopts a resolution increasing the number of agency members from five (5) to seven (7) resident electors as provided for in § 45-31-12, then the two (2) additional members shall be designated to serve for terms of one and two (2) years respectively. Thereafter members shall be appointed for a term of office of five (5) years, except that all vacancies occurring during a term shall be filled for the unexpired term. A member holds office until his or her successor has been appointed and has qualified.