I have already proved that for degree 2 homogenous linear recurrence relation of degree 2 that it's nth term can be expressed as A^n.C + B^n.D where C an D are constants which can be evaluated using given conditions and A and B are the roots of the characteristic equation.
How can I prove this for degree 3 and also for any k degree? Please give a detailed step-by-step solution because I could not extend my proof from degree 2 to degree 3.