Suppose the sequence a(n) satisfies the following divide-and-conquer recurrence: T(n) = 4T(n/2) + 10n; T(1) = 3. (a) Assuming n = 2k, fill in the recursion tree diagram below for T(n): help (numbers) Level 0 1 2 k = log₂ n Number of problems Problem size Work per problem Work per level 1 10n NOTE: Enter variable answers in terms of n. (b) Find a closed (explicit) formula for T(n). T(n) = 4 4^2 n n/2 n/4 1

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