Problem 1: (a) Give the general form of a linear homogeneous recurrence equation whose characteristic equation (after factoring) is (x+3)²(x − 2)²(x − 6) = 0. Justify your answer. (b) Consider the sequence defined by the recurrence: An = 3An-1-4An-3 with initial conditions Ao = 1, A₁ = −2 and A₂ = 0. Give the values of A₁ and A5. Show your work. (c) Consider the sequence defined by B₁ = 3.2" + 3", for all n ≥ 0. Give a complete homogeneous recurrence equation for B₁. Your equation must be of degree 2. Justify your answer.
Problem 1: (a) Give the general form of a linear homogeneous recurrence equation whose characteristic equation (after factoring) is (x+3)²(x − 2)²(x − 6) = 0. Justify your answer. (b) Consider the sequence defined by the recurrence: An = 3An-1-4An-3 with initial conditions Ao = 1, A₁ = −2 and A₂ = 0. Give the values of A₁ and A5. Show your work. (c) Consider the sequence defined by B₁ = 3.2" + 3", for all n ≥ 0. Give a complete homogeneous recurrence equation for B₁. Your equation must be of degree 2. Justify your answer.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Problem 1:
(a) Give the general form of a linear homogeneous recurrence equation whose characteristic
equation (after factoring) is (x+3)²(x - 2)²(x − 6) = 0. Justify your answer.
(b) Consider the sequence defined by the recurrence: An = 3An-1-44-3 with initial
conditions Ao = 1, A₁ = −2 and A₂ = 0. Give the values of A4 and A5. Show your work.
(c) Consider the sequence defined by B₁ 3.2 + 3n, for all n ≥ 0. Give a complete
homogeneous recurrence equation for B₁. Your equation must be of degree 2. Justify your
answer.
=
(d) Determine the form of a particular solution of each of the following recurrences:
(i) An = 2An-1 - An-2 + 3;
(ii) B₂ = 6B-1 -8Bn-2+2^(-3n² + 5);
(iii) Cn = 2Cn-2 +5n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccc4b4bb-a94d-4dc4-be7d-92733a14ab19%2Fa639dbb4-09ff-4635-a415-af4a0e65d39f%2Fn1qivog_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1:
(a) Give the general form of a linear homogeneous recurrence equation whose characteristic
equation (after factoring) is (x+3)²(x - 2)²(x − 6) = 0. Justify your answer.
(b) Consider the sequence defined by the recurrence: An = 3An-1-44-3 with initial
conditions Ao = 1, A₁ = −2 and A₂ = 0. Give the values of A4 and A5. Show your work.
(c) Consider the sequence defined by B₁ 3.2 + 3n, for all n ≥ 0. Give a complete
homogeneous recurrence equation for B₁. Your equation must be of degree 2. Justify your
answer.
=
(d) Determine the form of a particular solution of each of the following recurrences:
(i) An = 2An-1 - An-2 + 3;
(ii) B₂ = 6B-1 -8Bn-2+2^(-3n² + 5);
(iii) Cn = 2Cn-2 +5n.
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