A manufacturer of TV sets produced $600$ sets in the third year and $700$ sets in the seventh years. Assuming that the production increase uniformly by a fixed number every year, find the production in the first year.

A manufacturer of TV sets produced $600$ sets in the third year and $700$ sets in the seventh years. Assuming that the production increase uniformly by a fixed number every year, find the production in the ${10}^{\mathrm{th}}$ year.

A manufacturer of TV sets produced $600$ sets in the third year and $700$ sets in the seventh years. Assuming that the production increase uniformly by a fixed number every year, find the total production in the first $7$ years.