(1 point) Find the solution to the following recurrence: a_(n)=-8a_(n-1)-12a_(n-2)+441n for ngeqslant 2 with initial conditions a_(n)=

Question

(1 point) Find the solution to the following recurrence: a_(n)=-8a_(n-1)-12a_(n-2)+441n for ngeqslant 2 with initial conditions a_(n)=

Answer 1

To solve the given recurrence relation, we can use the method of solving linear homogeneous recurrence relations with constant coefficients.The given recurrence relation is:

for

We can rewrite this as:

Now, let's assume a solution of the form

, where

is a constant.Substituting this into the recurrence relation, we get:

Dividing both sides by

, we get:

Now, we can solve this quadratic equation to find the values of

.The quadratic equation is:

Solving this equation, we get:

and

Now, we can write the general solution of the recurrence relation as:

To find the values of

and

, we can use the initial conditions.Let's assume

and

as initial conditions.Substituting these values into the general solution, we get:

Solving this equation, we get:

Now, we can substitute this value of

into the general solution:

Simplifying this expression, we get:

To find the value of

, we can use the initial condition

.Substituting

into the expression for

, we get:

Solving this equation, we get:

Therefore, the solution to the given recurrence relation is:

So, the final answer is

.

Soru

(1 point) Find the solution to the following recurrence: a_(n)=-8a_(n-1)-12a_(n-2)+441n for ngeqslant 2 with initial conditions a_(n)=

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