The term of office of a council member shall begin at 7:30 P.M. on the first Monday in May following his or her election. The council shall hold a meeting at that time and the council member whose term is beginning shall be inducted into office. If a council member-elect fails to qualify within one month thereafter, his or her office shall become vacant. The council shall meet regularly at least monthly at such times as it may prescribe by ordinance or otherwise. The mayor or two (2) council members may call special meetings. All meetings of the council shall be open to the public and the journal of its proceedings shall be open to public inspection.