What is the sum of the first 1,000 consecutive odd numbers?

That is an arithmetic sequence of the form:

a (n) = 2n-1

Now the sum of an arithmetic sequence is just the average of the first and last terms times the number of terms ...

We know the first term is 1, let's find the last term ...

a (1000) = 2 (1000) - 1=1999

So the sum of that sequence is:

1000 (1999+1) / 2

1,000,000