**For each recurrence relation and initial conditions, find: (i) general solution; (ii) unique solution with the given initial conditions: (a) an = 3an−1 + 10an−2; a0 = 5, a1 = 11**

The **Answer to the Question**

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**Here's the Solution to this Question**

$a_{n}=3a_{n−1}+10a_{n−2}$$a_0=5$$a_1=11$

(i)

Characteristic equation: $r^2-3r-10=0$

$(r+2)(r-5)=0$Characteristic roots: $r_1=-2, r_2=5$

The general solution is

for some constants $\alpha_1$ and $\alpha_2.$

ii) Find the unique solution with the given initial conditions

The unique solution with the given initial conditions is