The City Council of the City of Harker Heights shall be composed of a Mayor and five City Councilmembers who shall be elected at large from the City for a term of three years. Such council shall be elected in the following manner subject to the adoption of this charter:
   Every year, in the second quarter, on a date prescribed by State law, either a Mayor and one councilmember, or two councilmembers as the case may be, will be elected by a majority vote to serve for a period of three years.
   No person shall serve for more than two consecutive three year terms in any one office, after the adoption of the charter.