Every mayor, councilman, and officer elected by the whole electorate of the city or town shall be a resident and qualified elector of the city or town in which he shall have been elected and shall reside within the limits of the city or town during his term of office. The councilmen shall be qualified electors of said city or town, residing within the limits of the ward from which they shall have been elected and shall reside within the limits of said ward during the term of their office.