GATE DIscrete Solve Recurrence Relation

Question

Solve the Recurrence Relation

S(r) - 6 S(r-1) +8 S(r-2) = 3^r;

S(0) =8,

S(1)=7

Answer 1

S(r) = c_1. 4ⁿ + c_2.2ⁿ   + 7.3ⁿ

Now, put the values of S(0) and S(1) to get c₁ and c₂

Comments

Can someone give a proper solution to this

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Can you please provide the theory to solve this question?

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When i solved, i got answer as:

S(r) = a.4^n + b.2^n   - 3^n+2

Where a = -8 and b = 25, and Particular value will be “-9”.

Answer 2

S(r)=((17)(2^r))-(3^(r+2)).   where r>=2 and S(0)=8 and S(1)=7