R.I. Gen. Laws § 45-50-6

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. Thereafter, members shall be appointed as aforesaid 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 shall hold office until his or her successor has been appointed and qualified; provided, however, that the provisions of this section shall not apply to an authority authorized pursuant to § 45-50-3(c), in which case the public law providing for the exercise of the powers of the authority by a body corporate and politic shall apply and be considered definitive.