I have the following recursive sequence an i want to find the general formula for the nth term of a sequence:
$$a_{n+2}=4a_{n+1}+4a_n,a_1=1,a_2=2$$
I have the following characteristic equation:
$x^2=4x+4$ but this has no integer zeroes so i do not know how to proceed with this.
Best Answer
there exists universal method of solving linear recurrences
for example in these topics
Linear Homogeneous Recurrence Relations and Inhomogenous Recurrence Relations
solving recurrence relations
Solving a Linear Recurrence Relation
it was described.
it is also in Wikipedia http://en.wikipedia.org/wiki/Recurrence_relation
or just google for "solving linear recurrence relations" or "solving homogeneous linear recurrence relations"