Question 2. Solve the recurrence relation 3an-1 + 6an-2 subject to the initial conditions ao = 1 and a1 = 5. an = 2. Solve the recurrence relation 3an-1 + 6an-2 subject to the initial conditions ao = 1 and a1 = 5. an =

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Transcribed Image Text: 2. Solve the recurrence relation 3an-1 + 6an-2 subject to the initial conditions ao = 1 and a1 = 5. an =
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Transcribed Image Text: 2. Solve the recurrence relation 3an-1 + 6an-2 subject to the initial conditions ao = 1 and a1 = 5. an =
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  2a_(m)=3a_(m-1)+6a_(m-2)avsiliary equation =>{:[=>r^(m)=3r^(m-1)+6r^(m-2)],[=>quadr^(2)-3r-6=0],[=>r=(3+-sqrt(9+24))/(2)],[r=(3+-sqrt33)/(2)],[" So, "quada_(n)=c_(1)((3+sqrt33)/(2))^(m)+c_(2)((3-sqrt33)/(2))^(m)],[rarrq_(0)=1=>c_(1)+c_(2)=1],[{:[rarrquada_(1)=5=>(3+sqrt33)c_(1)+(3-sqrt33)c_(2)=10],[" using (1) in (2) "=>],[=>(3+ ... See the full answer