find all solutions of the recurrence relation

Question

please any solve this sum from my engineering sem 3  subject dicreete mathematics

find all solutions of the recurrence relation

 

an = 5an-1  +  6an-2  + 7n

note for  5a(n-1)  in this (n-1) is to the base   same for 6a(n-2)  in this n-2 is to the base  and for 7n  in this n is to the power  

Answer 1

I’ve looked at this question and the answer is:

an = (1/7)(6^n + 6.(-1)^n).a0 + (1/7)(6^n – (-1)^n).a1 + (7/8)(7^(n+1) + (-1)^n)) – 7*6^n

It is possible to do this problem manually, but the amount of work required is quite a lot.

I notice that you are doing a maths course as part of an engineering degree. So I suspect that maybe you are supposed/expected to use a computer algebra package such as Mathematica, Maple, Matlab, ....

This would solve your problem with much greater ease.

Answer 2

Given an = 5a(n-1) + 6a(n-2) + 7n
an = 5an - 5a + 6an - 12a + 7n
an = 11an - 17a + 7n
an - 11an = 7n - 17a
-10 an = 7n - 17a
n = 1/7(17a-10)

Understand more about Recurrence Relation