Expert: Paul Klarreich - 10/9/2005

Question
We are working on geometric and arithmetic formulas, I can't seem to get a grasp on these. Can you help me put the following in a formula, and walk me through it? Please?
Find the sum of the first 5 odd positive integers?

Answer
Hi, Sandy,

The formulas you are talking about simply show a relationship between two quantities, such as the length of a side of a square and its area.

Your example is not really a case of a formula, just an arithmetic calculation.

But you want to do a good job on this, so you would write:
[VIEW IN A FIXED FONT]
The first odd positive integer is  1
The second..............           3
The third                          5
The fourth                         7
the fifth                          9

Those are the first five o. p. i.'s

Their sum is  1 + 3 + 5 + 7 + 9 = 25

(Hmmm.  The sum of the first four would be 16, wouldn't it?  And if you put on the sixth, 11, the sum would be 36.)

You might make an inspired guess about

The sum of the first n odd positive integers.

And THEN you would have a formula.