McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
Question
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Chapter 7.4, Problem 4AE
To determine

To compare the ratio to the golden ratio calculated in exercise 2 on page 253 and find whether there is a connection.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

The sequence 1, 1, 2, 3, 5, 8, 13, 21, … is called a Fibonacci sequence. The first two terms are 1 and 1. You then add two consecutive terms to get the next term.

Calculation:

The first two numbers for the new sequence are 3 and 11.

Hence the modified Fibonacci sequence will be

  3, 11, 14, 25, 39, 64, …

The following computer program computes the first 25 terms of the modified Fibonacci sequence shown above and finds the ratio of any term to its preceding term.

Let A, B, N, D, E, F, G and C be the variables used in program. Where A and B stand for the first two numbers in the sequence, N stands for the number of terms, D, E, F and G are used to find the ratio up to four decimal places, C stands for the next term in the sequence which is actually the sum of A and B. Consider the program below

Program:

'Print this statement "TERM NO. TERM RATIO" on output screen.

10 PRINT "TERM NO.", "TERM", "RATIO"

'Assign the first two terms to A and B

20 LET A=3

30 LET B=11

40 PRINT “1”, A,”-“

50 FOR N=2 TO 25

60 LET D=B/A

70 LET E=10000 × D

80 LET F=INT (E)

90 LET G=F/10000

100 PRINT N, B, G

110 LET C=B+A

120 LET A=B

130 LET B=C

140 NEXT N

'End of Program

150 END

Sample Output:

TERM NO. TERM RATIO

1 3 -

2 11 3.6666

3 14 1.2727

4 25 1.7857

5 39 1.56

6 64 1.641

7 103 1.6093

8 167 1.6213

9 270 1.6167

10 437 1.6185

11 707 1.6178

12 1144 1.6181

13 1851 1.618

14 2995 1.618

15 4846 1.618

16 7841 1.618

17 12687 1.618

18 20528 1.618

19 33215 1.618

20 53743 1.618

21 86958 1.618

22 140701 1.618

23 227659 1.618

24 368360 1.618

25 596019 1.618

Output Explanation:

Print the heading line for the table

TERM NO. TERM RATIO

Print the first term in the Fibonacci sequence

1 3 -

Print the remaining terms starting from term number 2 to term number 25

2 11 3.6666

3 14 1.2727

4 25 1.7857

5 39 1.56

6 64 1.641

7 103 1.6093

8 167 1.6213

9 270 1.6167

10 437 1.6185

11 707 1.6178

12 1144 1.6181

13 1851 1.618

14 2995 1.618

15 4846 1.618

16 7841 1.618

17 12687 1.618

18 20528 1.618

19 33215 1.618

20 53743 1.618

21 86958 1.618

22 140701 1.618

23 227659 1.618

24 368360 1.618

25 596019 1.618

The golden ratio calculated in the previous program was 1+52=1.618

The golden ratio computed in this exercise also is 1.618

Hence the ratio computed is similar to the given ratio.

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Chapter 7.4, Problem 3AE
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Chapter 7.4, Problem 1BE

Chapter 7 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 7.1 - Prob. 1CECh. 7.1 - Prob. 2CECh. 7.1 - Prob. 3CECh. 7.1 - Prob. 4CECh. 7.1 - Prob. 5CECh. 7.1 - Prob. 6CECh. 7.1 - Prob. 7CECh. 7.1 - Prob. 8CECh. 7.1 - Prob. 9CECh. 7.1 - Prob. 10CE
Ch. 7.1 - Prob. 11CECh. 7.1 - Prob. 12CECh. 7.1 - Prob. 13CECh. 7.1 - Prob. 14CECh. 7.1 - Prob. 15CECh. 7.1 - Prob. 16CECh. 7.1 - Prob. 17CECh. 7.1 - Prob. 18CECh. 7.1 - Prob. 1WECh. 7.1 - Prob. 2WECh. 7.1 - Prob. 3WECh. 7.1 - Prob. 4WECh. 7.1 - Prob. 5WECh. 7.1 - Prob. 6WECh. 7.1 - Prob. 7WECh. 7.1 - Prob. 8WECh. 7.1 - Prob. 9WECh. 7.1 - Prob. 10WECh. 7.1 - Prob. 11WECh. 7.1 - Prob. 12WECh. 7.1 - Prob. 13WECh. 7.1 - Prob. 14WECh. 7.1 - Prob. 15WECh. 7.1 - Prob. 16WECh. 7.1 - Prob. 17WECh. 7.1 - Prob. 18WECh. 7.1 - Prob. 19WECh. 7.1 - Prob. 20WECh. 7.1 - Prob. 21WECh. 7.1 - Prob. 22WECh. 7.1 - Prob. 23WECh. 7.1 - Prob. 24WECh. 7.1 - Prob. 25WECh. 7.1 - Prob. 26WECh. 7.1 - Prob. 27WECh. 7.1 - Prob. 28WECh. 7.1 - Prob. 29WECh. 7.1 - Prob. 30WECh. 7.1 - Prob. 31WECh. 7.1 - Prob. 32WECh. 7.1 - Prob. 33WECh. 7.1 - Prob. 34WECh. 7.1 - Prob. 35WECh. 7.1 - Prob. 36WECh. 7.2 - Prob. 1CECh. 7.2 - Prob. 2CECh. 7.2 - Prob. 3CECh. 7.2 - Prob. 4CECh. 7.2 - Prob. 5CECh. 7.2 - Prob. 6CECh. 7.2 - Prob. 7CECh. 7.2 - Prob. 8CECh. 7.2 - Prob. 9CECh. 7.2 - Prob. 10CECh. 7.2 - Prob. 11CECh. 7.2 - Prob. 12CECh. 7.2 - Prob. 13CECh. 7.2 - Prob. 14CECh. 7.2 - Prob. 15CECh. 7.2 - Prob. 16CECh. 7.2 - Prob. 1WECh. 7.2 - Prob. 2WECh. 7.2 - Prob. 3WECh. 7.2 - Prob. 4WECh. 7.2 - Prob. 5WECh. 7.2 - Prob. 6WECh. 7.2 - Prob. 7WECh. 7.2 - Prob. 8WECh. 7.2 - Prob. 9WECh. 7.2 - Prob. 10WECh. 7.2 - Prob. 11WECh. 7.2 - Prob. 12WECh. 7.2 - Prob. 13WECh. 7.2 - Prob. 14WECh. 7.2 - Prob. 15WECh. 7.2 - Prob. 16WECh. 7.2 - Prob. 17WECh. 7.2 - Prob. 18WECh. 7.2 - Prob. 19WECh. 7.2 - Prob. 20WECh. 7.2 - Prob. 21WECh. 7.2 - Prob. 22WECh. 7.2 - Prob. 23WECh. 7.2 - Prob. 24WECh. 7.2 - Prob. 25WECh. 7.2 - Prob. 26WECh. 7.2 - Prob. 27WECh. 7.2 - Prob. 28WECh. 7.2 - Prob. 29WECh. 7.2 - Prob. 30WECh. 7.2 - Prob. 31WECh. 7.2 - Prob. 32WECh. 7.2 - Prob. 33WECh. 7.2 - Prob. 34WECh. 7.2 - Prob. 35WECh. 7.2 - Prob. 36WECh. 7.2 - Prob. 37WECh. 7.2 - Prob. 38WECh. 7.2 - Prob. 39WECh. 7.2 - Prob. 40WECh. 7.2 - Prob. 41WECh. 7.2 - Prob. 42WECh. 7.2 - Prob. 43WECh. 7.3 - Prob. 1CECh. 7.3 - Prob. 2CECh. 7.3 - Prob. 3CECh. 7.3 - Prob. 4CECh. 7.3 - Prob. 5CECh. 7.3 - Prob. 6CECh. 7.3 - Prob. 7CECh. 7.3 - Prob. 8CECh. 7.3 - Prob. 9CECh. 7.3 - Prob. 10CECh. 7.3 - Prob. 1WECh. 7.3 - Prob. 2WECh. 7.3 - Prob. 3WECh. 7.3 - Prob. 4WECh. 7.3 - Prob. 5WECh. 7.3 - Prob. 6WECh. 7.3 - Prob. 7WECh. 7.3 - Prob. 8WECh. 7.3 - Prob. 9WECh. 7.3 - Prob. 10WECh. 7.3 - Prob. 11WECh. 7.3 - Prob. 12WECh. 7.3 - Prob. 13WECh. 7.3 - Prob. 14WECh. 7.3 - Prob. 15WECh. 7.3 - Prob. 16WECh. 7.3 - Prob. 17WECh. 7.3 - Prob. 18WECh. 7.3 - Prob. 19WECh. 7.3 - Prob. 20WECh. 7.3 - Prob. 21WECh. 7.3 - Prob. 22WECh. 7.3 - Prob. 23WECh. 7.3 - Prob. 24WECh. 7.3 - Prob. 25WECh. 7.3 - Prob. 26WECh. 7.3 - Prob. 27WECh. 7.3 - Prob. 28WECh. 7.3 - Prob. 29WECh. 7.3 - Prob. 30WECh. 7.3 - Prob. 31WECh. 7.3 - Prob. 32WECh. 7.3 - Prob. 33WECh. 7.3 - Prob. 34WECh. 7.3 - Prob. 35WECh. 7.3 - Prob. 36WECh. 7.3 - Prob. 37WECh. 7.3 - Prob. 1ST1Ch. 7.3 - Prob. 2ST1Ch. 7.3 - Prob. 3ST1Ch. 7.3 - Prob. 4ST1Ch. 7.3 - Prob. 5ST1Ch. 7.3 - Prob. 6ST1Ch. 7.3 - Prob. 7ST1Ch. 7.3 - Prob. 8ST1Ch. 7.3 - Prob. 9ST1Ch. 7.3 - Prob. 10ST1Ch. 7.3 - Prob. 11ST1Ch. 7.3 - Prob. 12ST1Ch. 7.3 - Prob. 13ST1Ch. 7.3 - Prob. 14ST1Ch. 7.3 - Prob. 15ST1Ch. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.4 - Prob. 1CECh. 7.4 - Prob. 2CECh. 7.4 - Prob. 3CECh. 7.4 - Prob. 4CECh. 7.4 - Prob. 5CECh. 7.4 - Prob. 6CECh. 7.4 - Prob. 7CECh. 7.4 - Prob. 8CECh. 7.4 - Prob. 9CECh. 7.4 - Prob. 10CECh. 7.4 - Prob. 11CECh. 7.4 - Prob. 12CECh. 7.4 - Prob. 13CECh. 7.4 - Prob. 1WECh. 7.4 - Prob. 2WECh. 7.4 - Prob. 3WECh. 7.4 - Prob. 4WECh. 7.4 - Prob. 5WECh. 7.4 - Prob. 6WECh. 7.4 - Prob. 7WECh. 7.4 - Prob. 8WECh. 7.4 - Prob. 9WECh. 7.4 - Prob. 10WECh. 7.4 - Prob. 11WECh. 7.4 - Prob. 12WECh. 7.4 - Prob. 13WECh. 7.4 - Prob. 14WECh. 7.4 - Prob. 15WECh. 7.4 - Prob. 16WECh. 7.4 - Prob. 17WECh. 7.4 - Prob. 18WECh. 7.4 - Prob. 19WECh. 7.4 - Prob. 20WECh. 7.4 - Prob. 21WECh. 7.4 - Prob. 22WECh. 7.4 - Prob. 23WECh. 7.4 - Prob. 24WECh. 7.4 - Prob. 25WECh. 7.4 - Prob. 26WECh. 7.4 - Prob. 27WECh. 7.4 - Prob. 28WECh. 7.4 - Prob. 29WECh. 7.4 - Prob. 30WECh. 7.4 - Prob. 31WECh. 7.4 - Prob. 32WECh. 7.4 - Prob. 33WECh. 7.4 - Prob. 34WECh. 7.4 - Prob. 35WECh. 7.4 - Prob. 1CCh. 7.4 - Prob. 2CCh. 7.4 - Prob. 1AECh. 7.4 - Prob. 2AECh. 7.4 - Prob. 3AECh. 7.4 - Prob. 4AECh. 7.4 - Prob. 1BECh. 7.4 - Prob. 2BECh. 7.4 - Prob. 3BECh. 7.4 - Prob. 4BECh. 7.5 - Prob. 1CECh. 7.5 - Prob. 2CECh. 7.5 - Prob. 3CECh. 7.5 - Prob. 4CECh. 7.5 - Prob. 5CECh. 7.5 - Prob. 6CECh. 7.5 - Prob. 7CECh. 7.5 - Prob. 8CECh. 7.5 - Prob. 9CECh. 7.5 - Prob. 1WECh. 7.5 - Prob. 2WECh. 7.5 - Prob. 3WECh. 7.5 - Prob. 4WECh. 7.5 - Prob. 5WECh. 7.5 - Prob. 6WECh. 7.5 - Prob. 7WECh. 7.5 - Prob. 8WECh. 7.5 - Prob. 9WECh. 7.5 - Prob. 10WECh. 7.5 - Prob. 11WECh. 7.5 - Prob. 12WECh. 7.5 - Prob. 13WECh. 7.5 - Prob. 14WECh. 7.5 - Prob. 15WECh. 7.5 - Prob. 16WECh. 7.5 - Prob. 17WECh. 7.5 - Prob. 18WECh. 7.5 - Prob. 19WECh. 7.5 - Prob. 20WECh. 7.5 - Prob. 21WECh. 7.5 - Prob. 22WECh. 7.5 - Prob. 23WECh. 7.5 - Prob. 1MRECh. 7.5 - Prob. 2MRECh. 7.6 - Prob. 1CECh. 7.6 - Prob. 2CECh. 7.6 - Prob. 3CECh. 7.6 - Prob. 4CECh. 7.6 - Prob. 5CECh. 7.6 - Prob. 6CECh. 7.6 - Prob. 7CECh. 7.6 - Prob. 8CECh. 7.6 - Prob. 9CECh. 7.6 - Prob. 1WECh. 7.6 - Prob. 2WECh. 7.6 - Prob. 3WECh. 7.6 - Prob. 4WECh. 7.6 - Prob. 5WECh. 7.6 - Prob. 6WECh. 7.6 - Prob. 7WECh. 7.6 - Prob. 8WECh. 7.6 - Prob. 9WECh. 7.6 - Prob. 10WECh. 7.6 - Prob. 11WECh. 7.6 - Prob. 12WECh. 7.6 - Prob. 13WECh. 7.6 - Prob. 14WECh. 7.6 - Prob. 15WECh. 7.6 - Prob. 16WECh. 7.6 - Prob. 17WECh. 7.6 - Prob. 18WECh. 7.6 - Prob. 19WECh. 7.6 - Prob. 20WECh. 7.6 - Prob. 21WECh. 7.6 - Prob. 22WECh. 7.6 - Prob. 23WECh. 7.6 - Prob. 24WECh. 7.6 - Prob. 25WECh. 7.6 - Prob. 26WECh. 7.6 - Prob. 27WECh. 7.6 - Prob. 28WECh. 7.6 - Prob. 29WECh. 7.6 - Prob. 30WECh. 7.6 - Prob. 31WECh. 7.6 - Prob. 32WECh. 7.6 - Prob. 33WECh. 7.6 - Prob. 1ST2Ch. 7.6 - Prob. 2ST2Ch. 7.6 - Prob. 3ST2Ch. 7.6 - Prob. 4ST2Ch. 7.6 - Prob. 5ST2Ch. 7.6 - Prob. 6ST2Ch. 7.6 - Prob. 7ST2Ch. 7.6 - Prob. 8ST2Ch. 7.6 - Prob. 9ST2Ch. 7.6 - Prob. 10ST2Ch. 7.6 - Prob. 11ST2Ch. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7 - Prob. 1CRCh. 7 - Prob. 2CRCh. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Prob. 11CRCh. 7 - Prob. 12CRCh. 7 - Prob. 13CRCh. 7 - Prob. 14CRCh. 7 - Prob. 15CRCh. 7 - Prob. 16CRCh. 7 - Prob. 17CRCh. 7 - Prob. 18CRCh. 7 - Prob. 19CRCh. 7 - Prob. 20CRCh. 7 - Prob. 21CRCh. 7 - Prob. 22CRCh. 7 - Prob. 23CRCh. 7 - Prob. 24CRCh. 7 - Prob. 1CTCh. 7 - Prob. 2CTCh. 7 - Prob. 3CTCh. 7 - Prob. 4CTCh. 7 - Prob. 5CTCh. 7 - Prob. 6CTCh. 7 - Prob. 7CTCh. 7 - Prob. 8CTCh. 7 - Prob. 9CTCh. 7 - Prob. 10CTCh. 7 - Prob. 11CTCh. 7 - Prob. 12CTCh. 7 - Prob. 13CTCh. 7 - Prob. 14CTCh. 7 - Prob. 15CTCh. 7 - Prob. 16CTCh. 7 - Prob. 1ARCh. 7 - Prob. 2ARCh. 7 - Prob. 3ARCh. 7 - Prob. 4ARCh. 7 - Prob. 5ARCh. 7 - Prob. 6ARCh. 7 - Prob. 7ARCh. 7 - Prob. 8ARCh. 7 - Prob. 9ARCh. 7 - Prob. 10ARCh. 7 - Prob. 11ARCh. 7 - Prob. 12ARCh. 7 - Prob. 13ARCh. 7 - Prob. 14ARCh. 7 - Prob. 15ARCh. 7 - Prob. 16ARCh. 7 - Prob. 17ARCh. 7 - Prob. 18ARCh. 7 - Prob. 19ARCh. 7 - Prob. 20ARCh. 7 - Prob. 21ARCh. 7 - Prob. 22ARCh. 7 - Prob. 23ARCh. 7 - Prob. 24ARCh. 7 - Prob. 25ARCh. 7 - Prob. 26ARCh. 7 - Prob. 27ARCh. 7 - Prob. 28ARCh. 7 - Prob. 29ARCh. 7 - Prob. 1CURCh. 7 - Prob. 2CURCh. 7 - Prob. 3CURCh. 7 - Prob. 4CURCh. 7 - Prob. 5CURCh. 7 - Prob. 6CURCh. 7 - Prob. 7CURCh. 7 - Prob. 8CURCh. 7 - Prob. 9CURCh. 7 - Prob. 10CURCh. 7 - Prob. 11CURCh. 7 - Prob. 1MCECh. 7 - Prob. 2MCECh. 7 - Prob. 3MCECh. 7 - Prob. 4MCECh. 7 - Prob. 5MCECh. 7 - Prob. 1ASNECh. 7 - Prob. 2ASNECh. 7 - Prob. 3ASNECh. 7 - Prob. 4ASNECh. 7 - Prob. 5ASNECh. 7 - Prob. 6ASNECh. 7 - Prob. 7ASNECh. 7 - Prob. 8ASNECh. 7 - Prob. 9ASNECh. 7 - Prob. 10ASNECh. 7 - Prob. 11ASNECh. 7 - Prob. 12ASNECh. 7 - Prob. 13ASNECh. 7 - Prob. 14ASNECh. 7 - Prob. 15ASNECh. 7 - Prob. 16ASNECh. 7 - Prob. 1CPECh. 7 - Prob. 2CPECh. 7 - Prob. 3CPECh. 7 - Prob. 4CPECh. 7 - Prob. 5CPECh. 7 - Prob. 6CPECh. 7 - Prob. 7CPECh. 7 - Prob. 8CPECh. 7 - Prob. 9CPECh. 7 - Prob. 1AECh. 7 - Prob. 2AECh. 7 - Prob. 3AECh. 7 - Prob. 4AECh. 7 - Prob. 5AECh. 7 - Prob. 6AECh. 7 - Prob. 7AECh. 7 - Prob. 8AECh. 7 - Prob. 9AECh. 7 - Prob. 10AECh. 7 - Prob. 11AECh. 7 - Prob. 12AECh. 7 - Prob. 13AECh. 7 - Prob. 14AECh. 7 - Prob. 15AECh. 7 - Prob. 1PECh. 7 - Prob. 2PECh. 7 - Prob. 3PECh. 7 - Prob. 4PECh. 7 - Prob. 5PECh. 7 - Prob. 6PE

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