Homework Answers
The characteristic function for the recurrence relation is given as:
x2 = -3 - 4x
=> x2 + 4x + 3 = 0
The roots of this equation are -1 and -3.
This means that
F(n) = a * (-1)n + b * (-3)n
Now, F(1) = -1 => -a - 3b = -1 => a + 3b = 1
And, F(2) = 7 => a + 9b = 7
Solving these two equations, we get
a = -2 and b = 1
Then, F(n) = -2 * (-1)n + (-3)n
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