Question

What is the solution for

an= -3an-1-3an-2-an-3, a0=1, a1=0, a2=5

a) (-1-4n+3n^2)(-1)^n
b) (1-4n-3n^2)(-1)^n
c) (1+4n+3n^2)(-1)^n

Answer 1

none of the above

(1 -4n +3n^2)(-1)^n

Explanation:

You have the recursive relation {a[0]=1, a[1]=0, a[2]=5, a[n]=-3a[n-1] -3a[n-2] -a[n-3]} and you want to know the explicit relation.

Test a few

The given initial value a[0] = 1 rules out choice A.

The value a[1] = 0 rules out choices B and C.

Actual solution

We observe that changing the sign of the constant in the first choice will make it match the sequence:

(1 -4n +3n^2)(-1)^n . . . . . . the solution for the recursive equation