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List the first 10 terms of each of these sequences.a) the

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

Solution for problem 5E 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 5E

List the first 10 terms of each of these sequences.

a) the sequence that begins with 2 and in which each successive term is 3 more that the preceding term

b) the sequence that lists each positive integer three limes, in increasing order

c) the sequence that lists the odd positive integers in increasing order, listing each odd integer twice

d) the sequence whose nth term is

e) the sequence that begins with 3, where each succeeding term is twice the preceding term

f) the sequence whose first term is 2. second term is 4, and each succeeding term is the sum of the two preceding terms

g) the sequence whose nth term is the number of bits in the binary expansion of the number n (defined in Section 4.2)

h) the sequence where the nth term is the number of letters in the English word for the index n

Step-by-Step Solution:
Step 1 of 3

Step-1:

 In this problem we need to find the first 10 terms of the sequences.

         a) The sequence begins with 2  and each successive term is 3 more that the preceding term.

          Let us consider  ,

                                     

                                     

                                     

                                     

                                          

                                     

                                     

                                     

                                       

       Therefore , the first 10 terms of the sequence is : 5 , 8, 11, 14 , 17 , 20 , 23 , 26 and 29.

Step-2:

   b)

      We know that the positive integers starts with  one.

       Let us consider , .

       , since sequence  that lists  each positive  integer three times , in increasing order.

 Then the next integer is  two.

 So, , since sequence  that lists  each positive  integer three times , in increasing order.

 Then the next integer is  three.

 So, , since sequence  that lists  each positive  integer three times , in increasing order.

 Tenth term is .

      Therefore , the first 10 terms of the sequence is : 1, 1, 1, 2, 2, 2, 3, 3, 3,  and 4.

Step-3:

         

  c)   We know that the  odd  positive integers starts with  one.

       Let us consider , .

      , since sequence  that lists  the odd positive integers  in increasing order , listing each odd integer twice.

      Then the next odd integer is three.

       So, , since sequence  that lists  the odd positive integers  in increasing order , listing each odd integer twice.

      Then the next odd integer is five.

       So, , since sequence  that lists  the odd positive integers  in increasing order , listing each odd integer twice.

      Then the next odd integer is seven.

       So, , since sequence  that lists  the odd positive integers  in increasing order , listing each odd integer twice.

      Then the next odd integer is nine

       So, , since sequence  that lists  the odd positive integers  in increasing order , listing each odd integer twice.

               Therefore , the first 10 terms of the sequence is : 1 , 1, 3,3,5,5,7,7,9 and 9.

Step-4:

     d)   Note : n! = (1)(2)(3)..........(n)

                     .

         

        Consider ,   term .

        If  n = 1 , then     

        If  n = 2 , then  .

         If  n = 3 , then  .

         If  n = 4 , then  .

          If  n = 5 , then  .

          If  n = 6 , then  

          If  n = 7 , then  

          If  n = 8 , then  

          If  n = 9 , then  

           If  n = 10 , then  .

 ...

Step 2 of 3

Chapter 2.4, Problem 5E is Solved
Step 3 of 3

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

Since the solution to 5E from 2.4 chapter was answered, more than 1398 students have viewed the full step-by-step answer. This full solution covers the following key subjects: term, sequence, whose, preceding, odd. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The full step-by-step solution to problem: 5E from chapter: 2.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “List the first 10 terms of each of these sequences.a) the sequence that begins with 2 and in which each successive term is 3 more that the preceding term________________b) the sequence that lists each positive integer three limes, in increasing order________________c) the sequence that lists the odd positive integers in increasing order, listing each odd integer twice________________d) the sequence whose nth term is ________________e) the sequence that begins with 3, where each succeeding term is twice the preceding term________________f) the sequence whose first term is 2. second term is 4, and each succeeding term is the sum of the two preceding terms________________g) the sequence whose nth term is the number of bits in the binary expansion of the number n (defined in Section 4.2)________________h) the sequence where the nth term is the number of letters in the English word for the index n” is broken down into a number of easy to follow steps, and 143 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7.

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