Question: 1- Consider the following recurrence relation T(0) = 4 T(1) = 10 T(n) = 6T(n - 1) - 8T(n - 2); n > 1 (a)

1- Consider the following recurrence relation T(0) = 4 T(1) = 10 T(n) = 6T(n - 1) - 8T(n - 2); n > 1 (a) Determine T(2); : : : ; T(5). (b) Solve the recurrence relation exactly. Show that your formula gives the correct value for T(5). (c) What Big-O class does this solution belong in?

2 - Consider the following recurrence relation T(0) = 4 T(1) = 10 T(n) = 6T(n - 1) - 8T(n - 2) - 6; n > 1 (a) Determine T(2); : : : ; T(5). (b) Solve the recurrence relation exactly. Show that your formula gives the correct value for T(5). NOTE: Feel free to use the results of the previous problem where appropriate.

3- Consider the following recurrence relation T(0) = 4 T(1) = 10 T(n) = 6T(n - 1) - 8T(n - 2) + 6n + 4; n > 1 (a) Determine T(2); : : : ; T(5). (b) Solve the recurrence relation exactly. Show that your formula gives the correct value for T(5). HINT: Let T(n) = S(n) + an + b, and select a and b such that the n term and the constant term drop out of the recurrence relation. Then solve for S(n), and in turn, T(n).

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