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### Sequence Differences

```Date: 06/24/2003 at 16:22:38
From: Anthony
Subject: Problem solving

The third and fourth terms of a sequence are 26 and 40. If the second
differences are a constant 4, what are the first five terms of the
sequence?
```

```
Date: 06/25/2003 at 08:20:22
From: Doctor Edwin
Subject: Re: Problem solving

Hi, Anthony.

I'm not sure where your difficulty is. Is it that you don't know
what "second differences" means, or that you don't know how to apply
it to this problem?

Let's talk about the terminology for a minute. "First difference" is
the difference between the numbers in the series. The series itself
looks like:

?   ?   26  40  ?

That is, we know two out of the five terms. So what's the first
difference between the third and fourth terms?

14      -- first difference
/ \
?   ?   26  40  ? -- series

Now the second difference is the difference between the first
differences. They've told us that it's 4 for all the terms:

4   4   4 -- second difference
/ \ / \ / \
?   ?  14   ? -- first difference
/ \ / \ / \ / \
?   ?   26  40  ? -- series

So what's the last first difference in our picture? It's going to be
4 more than the one before it, or 18:

4   4   4 -- second difference
/ \ / \ / \
?   ?  14  18 -- first difference
/ \ / \ / \ / \
?   ?   26  40  ? -- series

Which means that the last number in the series is 18 more than the
one before it. Is that enough to get you started? Write back if you
need more help.

- Doctor Edwin, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Sequences, Series

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