
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 21st, 2019, 11:46 PM  #1 
Member Joined: Nov 2012 Posts: 80 Thanks: 1  Recurrence relation
For second order linear homogeneous recurrence relation with constant coefficients, is it that the general sequence is only in the form of 1, t, t^2, t^3, ..., t^n or just one of the general sequences which satisfies the characteristic equation? Thank you.

February 22nd, 2019, 12:35 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,116 Thanks: 2331 
See this article.

February 22nd, 2019, 01:13 AM  #3 
Member Joined: Nov 2012 Posts: 80 Thanks: 1 
Thank you for the reference. It seems that the characteristic equation for a second order linear homogeneous recurrence relation with constant coefficients should be a Quadratic equation.

February 22nd, 2019, 07:40 AM  #4 
Member Joined: Nov 2012 Posts: 80 Thanks: 1 
Can I say that it is first assumed that the indexed term a(n)=t^n, and it happens that the assumption satisfies the recurrence relation by solving the characteristic equation?

February 22nd, 2019, 07:49 AM  #5 
Senior Member Joined: Dec 2015 From: Earth Posts: 832 Thanks: 113 Math Focus: Elementary Math 
Yes, it turns into a polynomial equation. But I donâ€™t know the reason behind it; let someone else prove it or give an article of proof. Last edited by skipjack; February 22nd, 2019 at 10:31 AM. 
February 22nd, 2019, 10:29 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,116 Thanks: 2331 
If the characteristic equation has distinct roots p and q, the nth term of the sequence is a(p^n) + b(q^n), where a and b are constants. 

Tags 
recurrence, relation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Recurrence Relation and Closed Form Relation  uniquegel  Algebra  4  September 8th, 2014 05:18 PM 
Recurrence relation  Joselynn  Real Analysis  2  September 14th, 2013 01:52 AM 
Recurrence Relation  roguebyte  Applied Math  1  April 15th, 2012 12:39 AM 
Recurrence Relation  ThatPinkSock52  Applied Math  1  February 20th, 2012 03:44 PM 
Recurrence Relation  roguebyte  Advanced Statistics  1  December 31st, 1969 04:00 PM 