f(n+2)=3f(n+1)-2f(n)

Question

Find the first five terms.

Answer 1

This is a 2nd degree difference equation and as such it has 2 initial conditions in the general solution.

You can only write the 1st five terms in terms of f(0) and f(1).

Now you can write out the terms this way: f(2)=3f(1)-2f(0) ad so on...or you can write the general solution which is

[f(1)-f(0)]*2ⁿ+2[f(0)-f(1)]