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### 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/
```
Associated Topics:
High School Sequences, Series

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