Mean of a Sequence

Date: 06/09/2002 at 12:55:10
From: Ana
Subject: What is the arithmetic mean of the first one thousand
positive odd numbers?

I've tried to figure out the answer in many different ways, like
finding the mean of the first 5 odd numbers, and the next 
5 odd numbers, to see if there is a pattern, but I get very stuck.
Thanks for trying to help.

Date: 06/09/2002 at 19:27:07
From: Doctor Ian
Subject: Re: What is the arithmetic mean of the first one thousand
positive odd numbers?

Hi Ana,

Starting small is exactly the right approach:

              1              mean = 1

             1 3             mean = 2
   
            1 3 5            mean = 3

           1 3 5 7           mean = 4

          1 3 5 7 9          mean = 5

         1 3 5 7 9 11        mean = 6

Do you see a pattern now? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 06/12/2002 at 20:54:40
From: Ana
Subject: Thank you (What is the arithmetic mean of the first one
thousand positive odd numbers?)

Thank you!