There is hereby created a Board of Housing Appeals of five members to conduct hearings authorized by this Housing Code. Members shall be appointed by the Mayor with approval of Council for overlapping terms of three years. Two of the first members shall be appointed for one year, two members for two years and one member for three years respectively, and they shall serve until a successor is appointed. To be eligible for appointment to such Board, a person shall be a citizen of the United States and a resident of the City.