My Math Forum  

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

Algebra Pre-Algebra and Basic Algebra Math Forum


Thanks Tree2Thanks
Reply
 
LinkBack Thread Tools Display Modes
November 10th, 2014, 12:44 PM   #1
Member
 
Joined: Jan 2013

Posts: 47
Thanks: 0

Super simple sequence question

Right so I've got myself in a right pickle on this question:
Find the nth term of
-2,-1,2,11

So I've tried using the standard an^2 + bn + c

But that hasn't worked ..

Any help??

Last edited by skipjack; November 10th, 2014 at 04:03 PM.
gazing600000 is offline  
 
November 10th, 2014, 12:52 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,087
Thanks: 2360

Math Focus: Mainly analysis and algebra
You will be able to make a cubic equation fit.
v8archie is online now  
November 10th, 2014, 01:02 PM   #3
Member
 
Joined: Jan 2013

Posts: 47
Thanks: 0

How would you do that?
gazing600000 is offline  
November 10th, 2014, 01:25 PM   #4
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
You can fit any n+1 points to an n-th degree equation -- this is the 'boring' solution. In your case I get
(2n^3 - 9n^2 + 16n - 15)/3
which you could get by solving an^3 + bn^2 + cn + d = y for each of the (x, y) pairs you have. It's a bit tiresome.
CRGreathouse is offline  
November 10th, 2014, 01:33 PM   #5
Member
 
Joined: Jan 2013

Posts: 47
Thanks: 0

got 4/6n^3 -3n^2 + 14 and 2/3 times n - 29/3

Any good?
gazing600000 is offline  
November 10th, 2014, 01:57 PM   #6
Member
 
Joined: Jan 2013

Posts: 47
Thanks: 0

Anyone else got an answer?
gazing600000 is offline  
November 10th, 2014, 02:35 PM   #7
Member
 
Joined: Jan 2013

Posts: 47
Thanks: 0

Someone must have a solution and answer!
gazing600000 is offline  
November 10th, 2014, 02:40 PM   #8
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,658
Thanks: 964

Math Focus: Elementary mathematics and beyond
You run out of room with differences ... so assume it's a cubic! Solve the system

a + b + c + d = -2
8a + 4b + 2c + d = -1
27a + 9b + 3c + d = 2
64a + 16b + 4c + d = 11

where a, b, c and d are the coefficients of the generating function.


By the way, please stop bumping.
greg1313 is online now  
November 10th, 2014, 03:08 PM   #9
Math Team
 
Joined: Apr 2010

Posts: 2,778
Thanks: 361

Another way, compute the differences.

Code:
-2  -1  2  11  
   1   3  9   
     2   6   
        4
Now, the interpolating polynomial is of the form
$\displaystyle a\cdot {n \choose 3} + b\cdot {n \choose 2}+c \cdot {n \choose 1}+d\cdot {n \choose 0}$
Then, look at the left 'column', having numbers -2, 1, 2 and 4. These are the values for a, b, c, d; (a, b, c, d) = (4, 2, 1, -2) to get
$\displaystyle 4\cdot {n \choose 3} + 2\cdot {n \choose 2}+1 \cdot {n \choose 1}-2\cdot {n \choose 0}$, which can be proved by induction.
You don't need to compute all difference to get these. Now, x in {0, 1, 2, 3} give the resulting elements from the sequence. An appropriate translation gives a desired offset (n->n-1).

Alternatively, the first differences are of the form 3^k, for k in {0, 1, 2}.
Summing them, with adding an extra constant, gives
(3^n-1)/2 - 2. n in {0, 1, 2, 3} produce the sequence.

Last edited by skipjack; November 10th, 2014 at 05:34 PM.
Hoempa is offline  
November 10th, 2014, 05:17 PM   #10
Global Moderator
 
Joined: Dec 2006

Posts: 18,235
Thanks: 1437

Or 2n! + n - 4, for n = 0, 1, 2 and 3.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
question, sequence, simple, super



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Super Simple mathd Elementary Math 2 May 9th, 2014 03:06 PM
Super basic question...pls help tek Algebra 3 October 5th, 2013 12:30 PM
4-th top Super User mathbalarka New Users 28 July 24th, 2013 09:14 AM
super simple algebra problem. questioner1 Algebra 5 July 2nd, 2012 10:59 PM
Simple, not so simple question about areas of triangles jkh1919 Algebra 1 November 20th, 2011 09:14 AM





Copyright © 2017 My Math Forum. All rights reserved.