My Math Forum Recurrence relation

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 21st, 2019, 10:46 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 21st, 2019, 11:35 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,379 Thanks: 2011 See this article. Thanks from justusphung and idontknow
 February 22nd, 2019, 12:13 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, 06:40 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, 06:49 AM #5 Senior Member   Joined: Dec 2015 From: iPhone Posts: 440 Thanks: 68 Yes, it turns into a polynomial equation. But I don’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 09:31 AM.
 February 22nd, 2019, 09:29 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,379 Thanks: 2011 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 Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post uniquegel Algebra 4 September 8th, 2014 04:18 PM Joselynn Real Analysis 2 September 14th, 2013 12:52 AM roguebyte Applied Math 1 April 14th, 2012 11:39 PM ThatPinkSock52 Applied Math 1 February 20th, 2012 02:44 PM roguebyte Advanced Statistics 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top