How do you find the arithmetic mean of the first one thousand positive odd numbers?

Answer 1

1000

Answer 2

The sum of all odd numbers, up to the odd number (2n-1) is

n^2. So the sum of the first 1000 or 10^3 odd positive numbers is (10^3)^2=10^6 Now divide by 10^3 or 1000 since we have 1000 numbers so we have 10^6/10^3=1000 The mean of the first 1000 positive odd numbers is 1000 If you ask the mean of the odd numbers between, 1 and 1000, that is another problem, since there are 500 of them, the answer would be 500^2/500=500 Think of the mean of the odd numbers between 1 and 10, there are 5 of them and there sum is 25 so the mean is 25/5 or 5 **** in general, the arithmetic mean of the first n odd numbers is n^2/n or n. So that is why the number is 1000.