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Find the solution to each of these recurrence relations

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 16E Chapter 2.4

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 16E

Find the solution to each of these recurrence relations with the given initial conditions. Use an iterative approach such as that used in Example 10.

Step-by-Step Solution:

Solution :Step 1:In this problem we have to find the solution for these recurrence relation, where we given the initial condition.a: let the recurrence relation is given as an = - an-1 with a0= 5Now we starting with initial condition a0 = 5 and working upward until we reach an to deduce a closed formula for the sequence. Then We put n = 0 ,1,2,3,4……...so on , Then a1= - a1-1 = - a0a1 = - 5a2 = - a2-1 = - a1a2 = - (-5)a2 = 5Now a3 = - a3-1 = - a2a3 = - 5a4 = - a4-1 = - a3 = -(- 5) a4 = 5Clearly we get alternate solutionsSo we can make the nth solution for this recurrence relation.an = (-1)n 5 .

Step 2 of 7

Chapter 2.4, Problem 16E is Solved
Step 3 of 7

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Find the solution to each of these recurrence relations