Wash. Rev. Code § 27.12.192
In any county with an adopted home rule charter and one million or more residents, the board of trustees of a rural county library district will be made up of seven members who are appointed by the county executive and confirmed by the county legislative authority. Members shall be residents of either those cities or towns that, through annexation, have become part of the rural county library district or unincorporated areas of the county, and that represent the geographic diversity of the library district. The composition of an initial seven-member rural county library district board of trustees will comprise the existing five trustees, who will serve out their existing terms, and two new trustees, whose positions shall have initial terms of one and two years respectively. Thereafter a trustee shall be appointed to serve for five years to fill each expired term. No person may be appointed to any board of trustees for more than two consecutive terms.
RCW 27.12.192