Find Sum of First Five Terms

Date: 03/26/2003 at 20:28:32
From: Jeff
Subject: Math problem

The 452nd term of an arithmetic sequence is -893 and the 84 is 27. 
Find the sum of the first five terms of the sequence.

I could solve this if the first term were given, or the common 
difference, but I have neither so I will need your help.

Date: 03/27/2003 at 00:06:04
From: Doctor Ian
Subject: Re: Math problem

Hi Jeff,

Let's look at a smaller version of the same problem:

   The 6th term of an arithmetic sequence is -5, and the
   3nd term is 1.  What are the first given terms of the
   sequence?

Now, it's true that I don't have the common difference, but I have
something almost as good. I have the difference between two terms
whose locations I know:

   __, __, 1, __, __, -5

If the common difference is d, then 

   1 + d + d + d = -5

         1 + 3*d = -5

             3*d = -6

               d = -2

So now I _do_ know the common difference, and with that, I can get
everything else. 

Does that make sense? Can you use the same reasoning to solve your
problem?   

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