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Find the first five terms of the sequence defined by each

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

Solution for problem 9E 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 9E

Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions.

a) 

b) 

c)

d) 

e) 

Step-by-Step Solution:
Step 1 of 3

Solution:

Step1

To find

 We have to find the first five terms of the sequence defined by each of these recurrence relations and initial conditions.

Step2

Sequence:-An arrangement is a specified collection of objects in which repetitions are permitted.

 Recurrence relations:-The technique for finding the terms of an arrangement in a recursive way is called  recurrence relations.

a.

First term

When n=1

Second term

     =

    = 6.2

    = 12

When n=2

Third term

      =

     = 6.12

    = 72

When n=3

Fourth term

      =

     = 6.72

    = 432

When n=4

Fifth term

      =

     = 6.432

    = 2592

Therefore,  the first five terms of the sequence defined by each of these recurrence relations and initial conditions is 2,12,72,432,2592.

Step3

b.

First term

When n=2

Second term

    =

    =

   =4

When n=3

Third term

    =

    =

   =16

When n=4

Fourth term

    =

    =

   =256

When n=5

Fifth term

    =

    =

   =65536

Therefore, the first five terms of the sequence defined by each of these recurrence relations and initial conditions is 2,4,16,256,65536.

Step4

c.

First term

Second term

When n=2

Third term

     =

    =2+3.1

     =2+3

    =5

When n=3

Fourth term

     =

    =5+3.2

     =5+6

    =11

When n=4

Fifth term

     =

    =11+3.5

     =11+15

    =26

Therefore, the first five terms of the sequence defined by each of these recurrence relations and initial conditions is 1,2,5,11,26.

Step5

d.

First term

Second term

When n=2

Third term

     =

     =2.1+4.1

    = 2+4

    =6

When n=3

Fourth term

     =

     =3.6+9.1

    = 18+9

    =27

When n=4

Fifth term

     =

     =4.27+16.6

    = 108+96

    =204

Therefore, the first five terms of the sequence defined by each of these recurrence relations and initial conditions is 1,1,6,27,204.

Step6

e.

First term

Second term

Third term

When n=3

Fourth term

  =

  = 0+1

   =1

When n=4

Fifth term

  =

  = 1+2

   =3

Therefore, the first five terms of the sequence defined by each of these recurrence relations and initial conditions is 1,2,0,1,3.

Step 2 of 3

Chapter 2.4, Problem 9E is Solved
Step 3 of 3

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

This full solution covers the following key subjects: conditions, defined, Find, initial, recurrence. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 9E from 2.4 chapter was answered, more than 1040 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The full step-by-step solution to problem: 9E from chapter: 2.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “?Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions.a) b) c) d) e)” is broken down into a number of easy to follow steps, and 22 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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