Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback
Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback
9th Edition
ISBN: 9780134469133
Author: Tannenbaum, Peter
Publisher: Prentice Hall
bartleby

Videos

Textbook Question
Chapter 13, Problem 1E

Compute the value of each of the following.

a. F 15

b. F 15 2

c. F 15 2

d. F 1515

e. F 15 / 5

Expert Solution
Check Mark
To determine

(a)

To calculate:

The value of F15.

Answer to Problem 1E

Solution:

The value of F15 is 610.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The Nth term of the Fibonacci sequence is denoted by FN.

Given:

The given expression is F15.

Formula used:

The recursive formula to calculate the Nth Fibonacci number is given by,

FN=FN1+FN2

Here FN1 and FN2 are the two preceding terms.

Calculation:

The 15th term in the sequence is the sum of 13th and 14th term. By using recursive formula,

FN=FN1+FN2

Substitute 1 for F1 and F2 in the above recursive formula to calculate F3,

F3=1+1=2

Substitute 1 for F2 and 2 for F3 to calculate F4,

F4=1+2=3

Substitute 2 for F3 and 3 for F4 to calculate F5,

F5=2+3=5

Similarly, F6=8, F7=13, F8=21, F9=34, F10=55, F11=89, F12=144, F13=233, and F14=377 are obtained.

Substitute F13 and F14 in the above recursive formula to calculate F15.

F15=233+377=610

Conclusion:

Thus, the 15th term in the sequence is 610.

Expert Solution
Check Mark
To determine

(b)

To calculate:

The value of F152.

Answer to Problem 1E

Solution:

The value of F152 is 608.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The Nth term of the Fibonacci sequence is denoted by FN.

Given:

The given expression is F152.

Formula used:

The recursive formula to calculate the Nth Fibonacci number is given by,

FN=FN1+FN2

Here FN1 and FN2 are the two preceding terms.

Substitute 610 for F15 from part (a) to calculate F152,

F152=6102=608

Conclusion:

Thus, the value of F152 is 608.

Expert Solution
Check Mark
To determine

(c)

To calculate:

The value of F152.

Answer to Problem 1E

Solution:

The value of F152 is 233.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The Nth term of the Fibonacci sequence is denoted by FN.

Given:

The given expression is F152.

Formula used:

The recursive formula to calculate the Nth Fibonacci number is given by,

FN=FN1+FN2

Here FN1 and FN2 are the two preceding terms.

In the Fibonacci sequence F152 is the 13th term of the sequence.

Substitute 89 for F11 and 144 for F12 from part (a) to calculate F13,

F13=89+144=233.

Conclusion:

Thus, the value of F152 is 233.

Expert Solution
Check Mark
To determine

(d)

To calculate:

The value of F1515.

Answer to Problem 1E

Solution:

The value of F1515 is 122.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The Nth term of the Fibonacci sequence is denoted by FN.

Given:

The given expression is F1515.

Formula used:

The recursive formula to calculate the Nth Fibonacci number is given by,

FN=FN1+FN2

Here FN1 and FN2 are the two preceding terms.

Substitute 610 for F15 from part (a) to get F1515,

F1515=61015=40.67

Conclusion:

Thus, the value of F1515 is 40.67.

Expert Solution
Check Mark
To determine

(e)

To calculate:

The value of F15/5.

Answer to Problem 1E

Solution:

The value of F15/5 is 2.

Explanation of Solution

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13 and so on, (each term is the sum of the first two preceding terms).

The terms of the Fibonacci sequence are known as Fibonacci numbers. The Nth term of the Fibonacci sequence is denoted by FN.

Given:

The given expression is F15/5.

Formula used:

The recursive formula to calculate the Nth Fibonacci number is given by,

FN=FN1+FN2

Here FN1 and FN2 are the two preceding terms.

The number F15/5 is the third term of the sequence given by,

F15/5=F3=F2+F1=1+1=2

Conclusion:

Thus, the value of F15/5 is 2.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 13 Solutions

Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback

Ch. 13 - Prob. 11ECh. 13 - Using a good calculator an online calculator if...Ch. 13 - Consider the following sequence of equations...Ch. 13 - Consider the following sequence of equations...Ch. 13 - Fact: If we make a list of any four consecutive...Ch. 13 - Fact: If we make a list of any 10 consecutive...Ch. 13 - Express each of the following as a single...Ch. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Prob. 20ECh. 13 - Prob. 21ECh. 13 - Prob. 22ECh. 13 - Prob. 23ECh. 13 - Prob. 24ECh. 13 - Consider the quadratic equation x2=x+1. a. Use the...Ch. 13 - Prob. 26ECh. 13 - Consider the quadratic equation 3x2=8x+5. a. Use...Ch. 13 - Prob. 28ECh. 13 - Prob. 29ECh. 13 - Prob. 30ECh. 13 - Consider the quadratic equation 21x2=34x+55. a....Ch. 13 - Prob. 32ECh. 13 - Prob. 33ECh. 13 - Consider the quadratic equation (FN2)x2=(FN1)x+FN,...Ch. 13 - The reciprocal of =1+52 is the rational number...Ch. 13 - The square of the golden ratio is the irrational...Ch. 13 - Given that F4998.61710103, a. find an approximate...Ch. 13 - Prob. 38ECh. 13 - Prob. 39ECh. 13 - Prob. 40ECh. 13 - Prob. 41ECh. 13 - Prob. 42ECh. 13 - Triangles T and T shown in Fig. 13-23 are similar...Ch. 13 - Polygons P and P shown in Fig. 13-24 are similar...Ch. 13 - Find the value of x so that the shaded rectangle...Ch. 13 - Find the value of x so that the shaded figure in...Ch. 13 - Prob. 47ECh. 13 - Prob. 48ECh. 13 - Prob. 49ECh. 13 - Prob. 50ECh. 13 - In Fig. 13-31 triangles BCA is a 36-36-108...Ch. 13 - Prob. 52ECh. 13 - Find the value of x of y so that in Fig. 13-33 the...Ch. 13 - Prob. 54ECh. 13 - Prob. 55ECh. 13 - Consider the sequence of ratios FN2FN. a. Using a...Ch. 13 - Prob. 57ECh. 13 - Prob. 58ECh. 13 - Prob. 59ECh. 13 - a.Explain what happens to the values of (152)N as...Ch. 13 - Prob. 61ECh. 13 - Prob. 62ECh. 13 - Prob. 63ECh. 13 - Prob. 64ECh. 13 - Prob. 65ECh. 13 - Find the value of x of y so that in Fig. 13-37 the...Ch. 13 - Prob. 67ECh. 13 - In Fig. 13-39 triangle BCD is a 727236 triangle...Ch. 13 - Prob. 69ECh. 13 - Prob. 70ECh. 13 - Prob. 71ECh. 13 - Prob. 72ECh. 13 - Prob. 73ECh. 13 - Prob. 74ECh. 13 - Prob. 75ECh. 13 - Prob. 76ECh. 13 - During the time of the Greeks the star pentagram...
Knowledge Booster
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Algebra: Structure And Method, Book 1
    Algebra
    ISBN:9780395977224
    Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
    Publisher:McDougal Littell
    College Algebra
    Algebra
    ISBN:9781938168383
    Author:Jay Abramson
    Publisher:OpenStax
    Algebra for College Students
    Algebra
    ISBN:9781285195780
    Author:Jerome E. Kaufmann, Karen L. Schwitters
    Publisher:Cengage Learning
  • Mathematics For Machine Technology
    Advanced Math
    ISBN:9781337798310
    Author:Peterson, John.
    Publisher:Cengage Learning,
  • Algebra: Structure And Method, Book 1
    Algebra
    ISBN:9780395977224
    Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
    Publisher:McDougal Littell
    College Algebra
    Algebra
    ISBN:9781938168383
    Author:Jay Abramson
    Publisher:OpenStax
    Algebra for College Students
    Algebra
    ISBN:9781285195780
    Author:Jerome E. Kaufmann, Karen L. Schwitters
    Publisher:Cengage Learning
    Mathematics For Machine Technology
    Advanced Math
    ISBN:9781337798310
    Author:Peterson, John.
    Publisher:Cengage Learning,
    12. Searching and Sorting; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=6LOwPhPDwVc;License: Standard YouTube License, CC-BY
    Algorithms and Data Structures - Full Course for Beginners from Treehouse; Author: freeCodeCamp.org;https://www.youtube.com/watch?v=8hly31xKli0;License: Standard Youtube License