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Higher order recurrence relations: Find the general solution to each recurrence (a) an −6an−1 + 11an−2...

Higher order recurrence relations:

Find the general solution to each recurrence

(a) an −6an−1 + 11an−2 −6an−3 = 0 for n ≥ 3.

(b) an −5an−2 + 4an−4 = 0 for n ≥ 4.

*hint*  To factor a polynomial of degree 3 or more look for a root r = a then use long division (dividing by the linear factor r −a) to find the cofactor (which will now be of degree one less). Repeat until you have factored completely into linear factors

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