R.I. Gen. Laws § 45-31-13: Tenure of agency members.

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.