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.

Hope this helps. If you have other questions about this or you're 
still stuck, please write back.

- 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.