# Help with recurrence relation

• Feb 10th 2010, 02:41 PM
jack11
Help with recurrence relation
I need to solve the following recurrence relations.

1. Homogeneous

A. an= 2an-1-an-2, for n> or equal to 2 and a0=4, a1=1

B. an+2= -4an-1+5an-2, for n> or equal to 2 and a0=2, a1=8

2. Non-homgogeneous

A. fn=3fn-1+n^2-3, n> or equal to 1; f0=1

B. fn+2+3fn+1+2fn=3n, n> or equal to 0; (f0,f1)=(0,1)

C. fn-4fn-1+4fn-2=3n+2^n, n> or equal to 2;(f0,f1)=(1,1)

D. an+3-3an+2+3an+1-an=3+5n, n> or equal to 0

Thanks.
• Feb 10th 2010, 02:57 PM
Drexel28
Quote:

Originally Posted by jack11
I need to solve the following recurrence relations.

1. Homogeneous

A. an= 2an-1-an-2, for n> or equal to 2 and a0=4, a1=1

B. an+2= -4an-1+5an-2, for n> or equal to 2 and a0=2, a1=8

2. Non-homgogeneous

A. fn=3fn-1+n^2-3, n> or equal to 1; f0=1

B. fn+2+3fn+1+2fn=3n, n> or equal to 0; (f0,f1)=(0,1)

C. fn-4fn-1+4fn-2=3n+2^n, n> or equal to 2;(f0,f1)=(1,1)

D. an+3-3an+2+3an+1-an=3+5n, n> or equal to 0

Thanks.

As I am sure you have probably surmised there is a wide variety of skill levels among the posters here on MHF. Consequently, before I help would you mind telling me your background?
• Feb 10th 2010, 03:21 PM
jack11
Hi, I am a software 3rd year student.
• Feb 10th 2010, 03:28 PM
Drexel28
Quote:

Originally Posted by jack11
Hi, I am a software 3rd year student.

...thank you for that. I meant, what is your background in recurrence relations. Could I just say "use the fact that every first-order homogenous linear recurrence relation is the sum of the roots of it's charcteristic equation to some power"?
• Feb 10th 2010, 04:15 PM
jack11
This is my first time dealing with recurrence relations. I tried to solve the questions by looking at some books but just kept getting stuck. Is it possible if someone can solve them...or atleast some of them. Thanks!
• Feb 10th 2010, 04:24 PM
Drexel28
Quote:

Originally Posted by jack11
This is my first time dealing with recurrence relations. I tried to solve the questions by looking at some books but just kept getting stuck. Is it possible if someone can solve them...or atleast some of them. Thanks!

See the last post. http://www.mathhelpforum.com/math-he...rsive-one.html