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### Arithmetic Sequence Conundrum

```Date: 10/11/2002 at 18:12:03
From: Peace Avery
Subject: Arithmetic Sequence Conundrum

I can't for the life of me get a handle on this problem. I have no
idea where to start.

For some real number T, the first three terms of an arithmetic
sequence are 2T, 5T - 1, and 6T + 2. What is the numerical value of
the fourth term?
```

```
Date: 10/11/2002 at 18:17:34
From: Doctor Achilles
Subject: Re: Arithmetic Sequence Conundrum

Hi Peace,

Thanks for writing to Dr. Math.

That's an interesting question. A simple arithmetic sequence is
something like:

13, 20, 27, 34, 41, 47, ...

It is arithmetic because the difference between each term is
constant (in this case, 7).

For any sequence to be arithmetic the difference between each two
consecutive terms must be constant.

For your sequence, the difference between the first two terms is:

(5T - 1) - 2T

And the difference between the second and third terms is:

(6T + 2) - (5T - 1)

Since it's arithmetic, you know that these two expressions must be
equal. So try making an equation and solving it for T.

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

```
Date: 10/11/2002 at 18:31:49
From: Peace Avery
Subject: Thank you (Arithmetic Sequence Conundrum)

It's all clear now, a thousand thanks. These SAT math questions have
a way of tripping me up, especially when the solution is so
straightforward. I really appreciate the help; one less thing to
worry about going in to the test tomorrow.
```
Associated Topics:
High School Basic Algebra
High School Sequences, Series

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