Which of the following sequences satisfies a second order linear homogeneous recurrence relation? O 3n+1 + n3"-1 O 2" + n3" n+1 n2 + 2n

b) Find the first five terms of the sequences described by the following recurrence relations. an = 3an-1 + 1 for n 2 2 a =2 an = 2an-1 - an-2 for n 23 aj = 3, a2 = 2

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Solve the first-order linear recurrence relation: Sn+1 = Sn + 2, with S0=1. You may use the general solution given on P.342.

Express the solution in big-O terms for the following recurrence relation: T(n) = 9*T(n/3) + n^3; T(1)=1; Answer: T(n) = O(......) .

Solve the first-order linear recurrence relation: Sn+1 = 5 Sn + 1, with S0=1. You may use the general solution given on P.342.

need help with x mark box

Question 4: Consider two recurrence relations P(n) = 2P(n/2) +n and Q(n) = 4Q (n/4) +2n. What is the relationship between P and Q? Is P = O(Q), P = N(Q), or P = O(Q)? Prove your answer using limit of ratio definition of asymptotic notations.

Consider the following recurrence relations: А. ТА(п) 2× TA(꽃) +n B. Tp(n) = 4 × Tâ() +n² C. Tc(n) = 8 × Tc()+n D. Tp(n) =8×Tp(플) + 1 and T4(1) = TB(1) = Tc(1) = Tp(1) = 0(1) || Problem: Assuming that each node in their respective recursion trees consume the same amount of constant space, which recurrence relation/s has/have the worst worst- case space complexity (O(M(n)))? Would this/these also require the most amount of space or program stack memory?

Solve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8