Suppose that you are given the roots to a characteristic

Question

Question: 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.