# Linear second-order recurrence sequences

1. Jan 15, 2008

### 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.

2. Jan 15, 2008

### 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.

3. Mar 14, 2008