In every city whose schools have been operating under special Acts and are governed by a board of school inspectors where such city, together with territory added thereto for school purposes, includes 2 districts for the purpose of electing 6 inspectors (3 in each district) and 1 district for all other school purposes, there shall continue to be elected a board of school inspectors, consisting of 6 members (3 in each district) and 1 inspector at large who shall be chosen for a term of 4 years. If 4 inspectors, excluding the inspector at large, are elected in 1983, those selected shall by lot determine one inspector to serve for 2 years and 3 for 4 years. Thereafter all terms shall be for 4 years.