At the first meeting of the planning commission, the seven (7) appointed members shall choose their term of office by lot as follows: one for one year; two (2) for two (2) years; two (2) for three (3) years and two (2) for four (4) years, and shall immediately thereafter notify the mayor and council in writing of such allotment. Their successors shall hold office for four (4) years, and any vacancy shall be filled by the mayor for the unexpired portion of the term. (1962 Code § 2-2-3)