Strategies for Tests on Sequences

Date: 7/9/96 at 20:56:8
From: Anonymous
Subject: Strategies for Tests on Sequences

On aptitude tests and the SAT, I have a problem with questions about 
number sequences. I'm good at everything else in math, but I get brain 
locked on these type of questions. Do you have any hints or practice 
aids that I can use?

Date: 7/10/96 at 10:2:16
From: Doctor Ethan
Subject: Re: Number sequence on tests

I have a few quick hints for you.

STEP ONE

   Ask yourself if the sequence looks as if it is growing slowly, 
   quickly, or in between.

   Here is an example of a sequence that is growing quickly:

      2, 9, 28, 65, 126,

   Here is an example of one that is growing slowly:

      2, 4, 6, 8, 10

   Here is one that's in between:

      2, 5, 10, 17, 26, 37, 50,


   If the sequence seem to be growing quickly, compare it to other 
   quick-growing sequences like the sequences of cubes or fourth 
   powers, or maybe factorials.

   If it is growing in between, compare it to the sequence of squares 
   or move to step 2.

   If it is growing slowly, move to step 2.

   If you can't tell, move to step 2.

STEP TWO

   Take your sequence and compare successive terms.

   Let's look at the in-between one. The first way to compare is to 
   see the difference between each one.

      +3  +5    +7   +9  +11  +13
     2   5   10   17   26   37   50

   Do you see a pattern?


   Sometimes the pattern of the differences isn't helpful. Look at

     3, 9, 27, 81

   If you can't recognize this sequence, differences won't help 
   you - but another trick will:

      +6  +18  +54
     3   9   27   81

   Another other trick is to look at multiples.

      *3  *3   *3   
     3   9   27   81

While these methods aren't foolproof, they will get you started. Good 
luck.

-Doctor Ethan,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/