Wednesday, November 11, 2009 - 10:26 AM

Here's a quick way to sum a sequential series of numbers.

If you want to add a sequential series of numbers you may do so by multiplying the exact middle number by the number of them to be added, such as:

10+11+12+13+14+15+16+17+18+19+20 = 15 x11 = 165

15 = the middle number in the series
11 = the number of numbers in the series

Notice the above sequence had an odd number of items, so it had an exact middle number. What about a sequential series with an even number of items? Simply take the average of the middle TWO numbers, like so:

26+27+28+29+30+31+32+33+34+35 = ((30 + 31)/2) x 10 = 30.5 x 10 = 305

30.5 = (30 + 31)/2 = the average of the middle two numbers in the series
10 = the number of numbers in the series

If you are familiar with statistics and the formula for the mean, you can probably figure out why this works using some simple algebra. It's a nice demonstration of how one can take a commonly used formula and rearrange it to give us another formula for something that is often tedious to compute by hand.