So I'm reviewing for an exam, and all the review question put up by the professor is as follows:

Solve.

$\displaystyle r_k = 2*r_{k-1} - r_{k-2}; r_0 = 1, r_1 = 4$

We didn't really cover this in class, and the example in the book is less than adequate, so I"m not sure what to do.

It says that a recurrence relation of the fom

$\displaystyle a_k = A* a_{k-1} + B * a_{k-2}$

Is satisfied by the sequence $\displaystyle 1, t, t^2...t^n$ if $\displaystyle t^2 - At - B = 0$

For this problem A = 2 and B = 0, which would make the equation

t^2 - 2t = 0

t(t-2) = 0

So the roots would be t = 0 and t = 2. So the only solution would be the sequence 1, 2, 4, 16... and 1, 0, 0, ...

Is that correct?