Linear second-order recurrence sequences

[feely]

Hello,

I hope I have posted this in the correct place, if not, sorry.

Okay, I have just started working through the material, but I am having some problems working out one of the examples, which is given below:

Un+2 = 12Un+1 - 20Un (n = 0,1,2...)

We are given
U0 = 1, U1 = 2

and are asked to work out U2 to U4.

But, maybe my head is just blocked, but I can't seem to get the figures. I have looked at the answers at the back of the book, but still no luck.

So, if anyone could point me in the right direction, I would be very thankful.

Cheers
Sean

PS - Sorry about typing the question out, I haven't got the hang of LaTeX just yet.

 

[dodo]

When n is 0, the line

$$U_{n+2} = 12 U_{n+1} - 20 U_n$$​

becomes

$$U_2 = 12 U_1 - 20 U_0$$​

n values of 1, 2, 3, ... will give you further terms of the sequence.

P.S.: You can click on the equations in this post, to see the corresponding LaTex for them.

 

[Fazza100]

Please go another step forward

What I would like to know is when n=1, and when n=2? What are the substitutions there then?