There is established a Board of Adjustment of the City comprised of five members, appointed by the Mayor and approved by the Council. Each member shall be a resident of the City. Membership of any member so appointed shall automatically terminate if the member ceases to be a resident of the City. A majority of the members of the Board shall be persons representing the public at large and shall not be involved in the business of purchasing or selling real estate. The term of appointment for each member shall be five years with the first Board serving for respective terms of five, four, three, two and one year in order to stagger the terms. Vacancies shall be filled by appointment for the unexpired term only.