Question : Solve the following difference equation p(n)=-2p(n-1)+8p(n-1)

Question : Solve the following difference equationp(n)=-2p(n-1)+8p(n-1) , p0=1, p_1 =1Solution :Given homogeneous linear difference equation \[ p_0=1,\ p_1=1,\] \[ p_n=-2p_{n-1}+8p_{n-2},\ \ n\geq2 \] \[p_n+2p_{n-1}-8p_{n-2}=0 \] (1) Replacing n by n+2 and taking n = 0, 1, 2, 3, 4,…

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