Proof of recurrence relations by induction

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Hi,
I have a question about proof of recurrence relations by induction. Is it fine to do them in a way that isn't in the mark scheme? For the ones where you have to prove it for n=1 and n=2 I do it for Uk=something and Uk-1=something. I then sub in n=k-1 into Uk+2=a(Uk+1)+b(Uk) to get Uk+1=a(Uk)+b(Uk-1). I then show it's true for n=k+1. And to finish I conclude it by saying: I have shown the proposition is true for n=1 and n=2 and that if it's true for n<=k then it's true for n=k+1. Therefore, by mathematical induction, it is true for (...).
Also I don't get it why for some recurrence relations you have to prove it for n=1 and n=2.
This is for FP1 Edexcel.
Any help is greatly appreciated.
Tom.

Unless I'm mistaken, what you're describing is the distinction between what's called "weak induction" and "strong induction". In the first case, you basically prove something for a base case - typically n = 1 - and then prove that if it's true for k then it's true for k+ 1. In the 2nd case, you prove 1 (or more) base case(s) and then show that being true for all positive integers <= some k is suffficient to prove the relation for k.

These are both valid techniques of induction, but I'd be surprised if FP1 requires you to use the more general version! Can you give us an example of a question where you've had trouble using the standard method?