recurrence relation

Question

T(K)=5T(K-1)-4T(K-2)   with initial condition T(0)=2  and  T(1)=3  determine T(10).

using recursion i got answer,but can anyone explain above method.

 

 

Comments

it is already well explained . I think you should go through some theory about it then you will get the solution.

First how to generate characteristic equation :- 

https://math.stackexchange.com/questions/166743/how-to-get-the-characteristic-equation

some theory about it:-

http://courses.ics.hawaii.edu/ReviewICS241/morea/counting/RecurrenceRelations2-QA.pdf

MIT video lecture Reference :-

https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/resources/lecture-15-linear-recurrences/

You can also kenneth rosen book for this as well.

Answer 1

 

Part 2 of the answer.

Hope this may help.

 

Answer 2

Characteristic root Technique.