My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 28th, 2015, 02:07 AM   #1
Newbie
 
Joined: Apr 2015
From: uk

Posts: 1
Thanks: 0

cubed number sequence

the sequence of cubed numbers increases by a sequence of numbers that differ by the six times table
ie
0,1,8,27,64
1,7,19,37 (the difference)
6,12,18,24 (the second row of difference)


my question is why is that?!
neilj is offline  
 
April 28th, 2015, 03:04 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,474
Thanks: 2039

As the original numbers are cubes, the first differences are given by a quadratic expression and the second differences by a linear expression. It happens to be the case that this linear expression has no constant term, so the second differences form a times table.

Had you started with cube plus square, you would have got
0, 2, 12, 36, 80, . . .
2, 10, 24, 44, . . . (first differences)
8, 14, 20, . . . (second differences)
so the second differences no longer form a times table.

Note that if you start with nth powers, the nth differences all equal n factorial.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
cubed, number, sequence



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help on number sequence thei Number Theory 6 September 11th, 2013 09:06 PM
What's the next number of this sequence miket Number Theory 0 November 7th, 2010 03:06 AM
Possible number of N-number sequence in ascending order conjecture Applied Math 5 April 13th, 2008 10:57 AM
Number Sequence (2) johnny Number Theory 9 April 13th, 2008 06:25 AM
Number Sequence johnny Number Theory 4 April 9th, 2008 06:07 AM





Copyright © 2019 My Math Forum. All rights reserved.