Im hoping you guys could point me in the right direction after getting myself rather lost with a question on my assignment. I am not putting the actual question as i would like to work it out myself. here is a question i have made up that is similar with what i think to be correct. Could anyone verify this or point me in the right direction?
Let Fn be the Fibonacci sequence.
Use the Fibonacci recurrence relation to express Fn+3 in terms of Fn+1 and Fn. Hence show that Fn+1 = 1/2(Fn+5 - Fn) for n=0,1,2,...
the next question i have is the same but with Fn+1 = 1/2(Fn+5 + Fn)
then i have to decide wether the formulas would remain true if the sequence Fn were replaced by a sequence with the same recurrence relation as the Fibonacci sequence but with different initial terms, then justify.
So if i look just at the 1st one at the moment, i think that i would get something like this;
Fn+1 = 1/2(Fn+5 - Fn) for n=0,1,2,...
Fn = 1/2(Fn+1 - Fn+1)
Fn = 1/2(Fn+2 + Fn+1)
if that is not correct, how do i work this out properly as im rather stumped :-S