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Finding the Pattern in a Series of Numbers

Date: 11/14/95 at 19:15:13
From: Anonymous
Subject: Pattern for 1, 8, 27...

What is the pattern for 1, 8, 27... ?

Date: 11/14/95 at 20:3:30
From: Doctor Ethan
Subject: Re: Pattern for 1, 8, 27...

Hello -

You ask for the pattern that explains the list:

1, 8, 27, 64, 125, .....

Here is my suggestion.

Find the factors of each of the numbers and look for a pattern in them.

Hope this helps,

-Doctor Ethan,  The Geometry Forum

Date: 11/15/95 at 13:08:13 
From: "Thomas H. Haule"
Subject: More help RE: pattern for 1, 8, 27...

Dr. Ethan,  

Thank you for your reply.  Unfortunately it has not helped.  The question I 
submitted was part of my daughter's 4th grade math homework.  She came 
to me for help and despite my 44 years of age and experience, (including a 
B.A. some years back) I have been unable to provide any help on this one.  

My wife and I have been tangling with concepts such as "if you add the first 
two and multiply by the position of the third it yields 27, but that doesn't 
help for the next two numbers you have provided.  I assure you we are not 
school kids trying to pull a scam on our teacher.  We are parents completely 
at a loss as to what to tell our 9-year old.  Please help.

P.S.  my wife and I are both writers and have leaned on the right sides of our 
brains for too long.

--Tom Haule, Joan Haule

Date: 11/17/95 at 16:21:19 
From: "Dr. Math"
Subject: Re: More help RE: pattern for 1, 8, 27...

Thanks for the reply.  I will be more explicit.  I still don't want to just 
give the answer but I will try to spell out the steps more carefully.

To factor a number like 6 you look for the numbers it takes to get six via 

so   6 = 2 * 3
and 12 = 2 * 2 * 3

We wouldn't accept 12 = 3 * 4 because 4 can be factored further.

Consider 32 = 2*16 = 2*2*8 = 2*2*2*4 = 2*2*2*2*2

- that is as factored as it gets.

So, for our series:

   1 has no factors

   8 has 2*2*2

   What do 27 and 64 have? 

   Then 125?  (64 might confuse you so be sure to go on and look at 125.)

Good luck and write back if you are still stuck.

Doctor Ethan

Date: 11/19/95 at  07:23:05
From: "Thomas H. Haule"
Subject: Doctor Ethan's Reply

Dr. Ethan:

We received your second reply to our inquiry regarding the pattern for the 
numbers 1, 8, 27....Comprehension's light bulb ignited!  A resounding 
"HAW-HEE" burst forth from the back of my brain as the simplicity of the 
problem became apparent.  It's my way of saying how completely stupid I 
felt when I realized the answer:  1-cubed, 2-cubed, 3-cubed etc.  

Thank you for your time and patience with such an elementary concept.  
We have been able to use your approach to have our daughter work through 
the solution. 

Again thank you for your help.

Thomas H. Haule
Associated Topics:
High School Sequences, Series

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