If the city's population has grown by 1,000 people in the last 2 years, then the average growth rate per year is 1000/2 = <<1000/2=500>>500 people/year.
Therefore, in 6 years, the city will grow by 500*6 = <<500*6=3000>>3000 people. Answer: \boxed{3000}.
A city's population has grown by 1,000 people in the last 2 years. On average, how many people will the city grow by in 6 years?
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