Thread: 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.

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?

Hi, I am a software 3rd year student.

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"?

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!

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