Is there a short cut to avoid typing multiple formulae?

I'm a relative novice in using Excel so pardon me for the layman lingo used here.
Consider this scenario:

A B C
1 10 12
2 12 14
3 14 16
4 16 18
5 18 20
6 20 22
7 22 24
8 . .
. . .
. . .
. . .
. . .
. . .


I want to compute the average of the values in the A and B columns. So in cell C1, I type the formula =AVERAGE(A1:B1) to obtain the average. But now I have thousands of cells to compute, so how do I go about doing so without having to manually type the formula in the respective C cells?

oops wrong layout there, the 2nd number column should be under A and the 3rd number column should be under B.

Thanks

In C1 where you have your formula, move your mouse coursor to the bottom right corner of the cell (where you see the small black box). When your cursor is over that box it will change to a + sign. When it is a + sign left click and while holding down the left mouse button drag it down the C column as far as you need the formula to be repeated. When you reach the last cell in C column let go of the left mouse button. Your formula will now be filled down.