Consider the following recurrence relation and initial conditions. bk = 9bk − 1 − 18bk − 2, for every integer k ≥ 2 b0 =

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Consider the following recurrence relation and initialconditions. bk = 9bk − 1 − 18bk − 2, for every integer k ≥ 2 b0 =2, b1 = 4 (a) Suppose a sequence of the form 1, t, t2, t3, , tn ,where t ≠ 0, satisfies the given recurrence relation (but notnecessarily the initial conditions). What is the characteristicequation of the recurrence relation? Correct: Your answer iscorrect. What are the possible values of t? (Enter your answer as acomma-separated list.) t = Correct: Your answer is correct. (b)Suppose a sequence b0, b1, b2, satisfies the given initialconditions as well as the recurrence relation. Fill in the blanksbelow to derive an explicit formula for b0, b1, b2, in terms of n.It follows from part (a) and the distinct roots theorem that forsome constants C and D, the terms of b0, b1, b2, satisfy theequation bn = Correct: Your answer is correct. for every integer n≥ 0. Solve for C and D by setting up a system of two equations intwo unknowns using the facts that b0 = 2 and b1 = 4. The result isthat bn = Incorrect: Your answer is incorrect. for every integer n≥ 0.

Consider The Following Recurrence Relation And Initial Conditions Bk 9bk 1 18bk 2 For Every Integer K 2 B0 1 (96 KiB) Viewed 38 times

Consider the following recurrence relation and initial conditions. 18bk - 2, for every integer k ≥ 2 bk = 9bk-1- bo - = 2, b₁ = 4 (a) Suppose a sequence of the form 1, t, t², t³, + where t = 0, satisfies the given recurrence relation (but not necessarily the initial conditions). What is the characteristic equation of the recurrence relation? t²-9t+18=0 What are the possible values of t? (Enter your answer as a comma-separated list.) t = 3,6 (b) Suppose a sequence bo, b₁,b₂, satisfies the given initial conditions as well as the recurrence relation. Fill in the blanks below to derive an explicit formula for bo, b₁,b₂, in terms of n. It follows from part (a) and the distinct ✓roots theorem that for some constants C and D, the terms of bo, b₁ b₂₁ satisfy the equation b, C.3n+D.6h for every integer n ≥ 0. = Solve for C and D by setting up a system of two equations in two unknowns using the facts that bo = 2 and b₁ = 4. The result is that bn for every integer n ≥ 0. =