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Suppose that you are given the roots to a characteristic equation, and they are -1,2, and -3.
(a) What is the characteristic equation?
(b) To what recurrence does that correspond?
(c) Find initial conditions so that an = (-1)n is the closed form for the recurrence. Use the recurrence to generate a few more terms to be sure your initial conditions work.
(d) Find initial conditions so that an = (-1)n + 2n is the closed form for the recurrence. Use the recurrence to generate three additional terms to be sure your initial conditions work.
(e) Find initial conditions so that an = (-1)n + 2n + (-3)n is the closed form for the recurrence. Use the recurrence to generate three additional terms to be sure your initial conditions work.
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