How to find the close form of
$a_n =\frac{1}{8}a_{n-2} -\frac{1}{4}a_{n−1}$ given that $a_1 = 0, a_2 = -1$?

Question

ikram002p · Answer

what is a_0 and a_1 ?
or any initial a's ?

anonymous · Answer

a_0 = 0, a_1 = -1

ikram002p · Answer

ok , expand only
unfortunately I have to go cuz I have a class brb

hartnn · Answer

get a_2 , a_3 ... and search for pattern...
I'll think about an alternate approach..

anonymous · Answer

Edit:
a1 = 0, a2 = -1, a3 = 1/4, a4 = -3/16

anonymous · Answer

I would like to know if there is a systematic way to solve such difference equation.

hartnn · Answer

are you expecting something like this : 
$\Large a_n = (-1/4)a_{n-1} + (1/8-1/4)\sum \limits_{i=2}^{n-2}a_i+(1/8)a_1 $

anonymous · Answer

Ehm.. Not really...

hartnn · Answer

ok, in terms of n only

anonymous · Answer

Yup!

experimentx · Answer

sorry .. i forgot to reply.
do you know z-transform?

anonymous · Answer

I learnt it in EEE 2 years ago, but forgot most of it

experimentx · Answer

there are two ways of doing it .. actually three. 
#1 find out the general pattern as you list the terms.
#2 use z-transform
#3 FInd the eiven vectors and the eigen values of the equation
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