exactly, and after you get the constant coefficients you can solve the homogeneous equation to find Qn.
Given that the following sequence, Q_{n} , satisfies a homogeneous second order difference equation with constant coefficients find Q_{n} :
I reckon that it would have to start with and do i then just put in the various numbers and solve them simultaneiously?
I'm sorry if I sound rude, but if you deal with a topic in "advanced" algebra such as difference equations you must at least know how to solve a system of linear equations. If you don't know or forgot, there are plenty of resources on the internet such as:
System of linear equations - Wikipedia, the free encyclopedia
Nah you wern't rude by any means, its just i get given work that hasnt been explained properly, i then look at the notes and the examples are really poor, and so out of frustration i forget how to do the simplest of things.
But, through simultaneous equations i keep getting -
-5A - 5B = 0
-5A - 5B = 0
Which gets me nowhere.. Or at least i think..
to get the first equation substitute n=3:
now n=4:
now n=5:
as you can see the third equation is the sum of the forst two, so the equations are linearly dependent, that's why you had a problem.
after solving the system we get that the general solution is:
A = -B = -C
let's choose A=1, B=C=-1
thus:
you can notice that we've got the fibonacci sequence.