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

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Chapter 7.4, Problem 2AE

To determine

To modify the program and run it by changing line 20 and 30 and also find what happens to the values of the ratios as the terms become larger and larger.

Expert Solution & Answer

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

As the terms become larger, the ratio converges to the value 1.618

Chapter 7.4, Problem 1AE

Chapter 7.4, Problem 3AE

Chapter 7 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 7.1 - Prob. 1CE Ch. 7.1 - Prob. 2CE Ch. 7.1 - Prob. 3CE Ch. 7.1 - Prob. 4CE Ch. 7.1 - Prob. 5CE Ch. 7.1 - Prob. 6CE Ch. 7.1 - Prob. 7CE Ch. 7.1 - Prob. 8CE Ch. 7.1 - Prob. 9CE Ch. 7.1 - Prob. 10CE

Ch. 7.1 - Prob. 11CE Ch. 7.1 - Prob. 12CE Ch. 7.1 - Prob. 13CE Ch. 7.1 - Prob. 14CE Ch. 7.1 - Prob. 15CE Ch. 7.1 - Prob. 16CE Ch. 7.1 - Prob. 17CE Ch. 7.1 - Prob. 18CE Ch. 7.1 - Prob. 1WE Ch. 7.1 - Prob. 2WE Ch. 7.1 - Prob. 3WE Ch. 7.1 - Prob. 4WE Ch. 7.1 - Prob. 5WE Ch. 7.1 - Prob. 6WE Ch. 7.1 - Prob. 7WE Ch. 7.1 - Prob. 8WE Ch. 7.1 - Prob. 9WE Ch. 7.1 - Prob. 10WE Ch. 7.1 - Prob. 11WE Ch. 7.1 - Prob. 12WE Ch. 7.1 - Prob. 13WE Ch. 7.1 - Prob. 14WE Ch. 7.1 - Prob. 15WE Ch. 7.1 - Prob. 16WE Ch. 7.1 - Prob. 17WE Ch. 7.1 - Prob. 18WE Ch. 7.1 - Prob. 19WE Ch. 7.1 - Prob. 20WE Ch. 7.1 - Prob. 21WE Ch. 7.1 - Prob. 22WE Ch. 7.1 - Prob. 23WE Ch. 7.1 - Prob. 24WE Ch. 7.1 - Prob. 25WE Ch. 7.1 - Prob. 26WE Ch. 7.1 - Prob. 27WE Ch. 7.1 - Prob. 28WE Ch. 7.1 - Prob. 29WE Ch. 7.1 - Prob. 30WE Ch. 7.1 - Prob. 31WE Ch. 7.1 - Prob. 32WE Ch. 7.1 - Prob. 33WE Ch. 7.1 - Prob. 34WE Ch. 7.1 - Prob. 35WE Ch. 7.1 - Prob. 36WE Ch. 7.2 - Prob. 1CE Ch. 7.2 - Prob. 2CE Ch. 7.2 - Prob. 3CE Ch. 7.2 - Prob. 4CE Ch. 7.2 - Prob. 5CE Ch. 7.2 - Prob. 6CE Ch. 7.2 - Prob. 7CE Ch. 7.2 - Prob. 8CE Ch. 7.2 - Prob. 9CE Ch. 7.2 - Prob. 10CE Ch. 7.2 - Prob. 11CE Ch. 7.2 - Prob. 12CE Ch. 7.2 - Prob. 13CE Ch. 7.2 - Prob. 14CE Ch. 7.2 - Prob. 15CE Ch. 7.2 - Prob. 16CE Ch. 7.2 - Prob. 1WE Ch. 7.2 - Prob. 2WE Ch. 7.2 - Prob. 3WE Ch. 7.2 - Prob. 4WE Ch. 7.2 - Prob. 5WE Ch. 7.2 - Prob. 6WE Ch. 7.2 - Prob. 7WE Ch. 7.2 - Prob. 8WE Ch. 7.2 - Prob. 9WE Ch. 7.2 - Prob. 10WE Ch. 7.2 - Prob. 11WE Ch. 7.2 - Prob. 12WE Ch. 7.2 - Prob. 13WE Ch. 7.2 - Prob. 14WE Ch. 7.2 - Prob. 15WE Ch. 7.2 - Prob. 16WE Ch. 7.2 - Prob. 17WE Ch. 7.2 - Prob. 18WE Ch. 7.2 - Prob. 19WE Ch. 7.2 - Prob. 20WE Ch. 7.2 - Prob. 21WE Ch. 7.2 - Prob. 22WE Ch. 7.2 - Prob. 23WE Ch. 7.2 - Prob. 24WE Ch. 7.2 - Prob. 25WE Ch. 7.2 - Prob. 26WE Ch. 7.2 - Prob. 27WE Ch. 7.2 - Prob. 28WE Ch. 7.2 - Prob. 29WE Ch. 7.2 - Prob. 30WE Ch. 7.2 - Prob. 31WE Ch. 7.2 - Prob. 32WE Ch. 7.2 - Prob. 33WE Ch. 7.2 - Prob. 34WE Ch. 7.2 - Prob. 35WE Ch. 7.2 - Prob. 36WE Ch. 7.2 - Prob. 37WE Ch. 7.2 - Prob. 38WE Ch. 7.2 - Prob. 39WE Ch. 7.2 - Prob. 40WE Ch. 7.2 - Prob. 41WE Ch. 7.2 - Prob. 42WE Ch. 7.2 - Prob. 43WE Ch. 7.3 - Prob. 1CE Ch. 7.3 - Prob. 2CE Ch. 7.3 - Prob. 3CE Ch. 7.3 - Prob. 4CE Ch. 7.3 - Prob. 5CE Ch. 7.3 - Prob. 6CE Ch. 7.3 - Prob. 7CE Ch. 7.3 - Prob. 8CE Ch. 7.3 - Prob. 9CE Ch. 7.3 - Prob. 10CE Ch. 7.3 - Prob. 1WE Ch. 7.3 - Prob. 2WE Ch. 7.3 - Prob. 3WE Ch. 7.3 - Prob. 4WE Ch. 7.3 - Prob. 5WE Ch. 7.3 - Prob. 6WE Ch. 7.3 - Prob. 7WE Ch. 7.3 - Prob. 8WE Ch. 7.3 - Prob. 9WE Ch. 7.3 - Prob. 10WE Ch. 7.3 - Prob. 11WE Ch. 7.3 - Prob. 12WE Ch. 7.3 - Prob. 13WE Ch. 7.3 - Prob. 14WE Ch. 7.3 - Prob. 15WE Ch. 7.3 - Prob. 16WE Ch. 7.3 - Prob. 17WE Ch. 7.3 - Prob. 18WE Ch. 7.3 - Prob. 19WE Ch. 7.3 - Prob. 20WE Ch. 7.3 - Prob. 21WE Ch. 7.3 - Prob. 22WE Ch. 7.3 - Prob. 23WE Ch. 7.3 - Prob. 24WE Ch. 7.3 - Prob. 25WE Ch. 7.3 - Prob. 26WE Ch. 7.3 - Prob. 27WE Ch. 7.3 - Prob. 28WE Ch. 7.3 - Prob. 29WE Ch. 7.3 - Prob. 30WE Ch. 7.3 - Prob. 31WE Ch. 7.3 - Prob. 32WE Ch. 7.3 - Prob. 33WE Ch. 7.3 - Prob. 34WE Ch. 7.3 - Prob. 35WE Ch. 7.3 - Prob. 36WE Ch. 7.3 - Prob. 37WE Ch. 7.3 - Prob. 1ST1 Ch. 7.3 - Prob. 2ST1 Ch. 7.3 - Prob. 3ST1 Ch. 7.3 - Prob. 4ST1 Ch. 7.3 - Prob. 5ST1 Ch. 7.3 - Prob. 6ST1 Ch. 7.3 - Prob. 7ST1 Ch. 7.3 - Prob. 8ST1 Ch. 7.3 - Prob. 9ST1 Ch. 7.3 - Prob. 10ST1 Ch. 7.3 - Prob. 11ST1 Ch. 7.3 - Prob. 12ST1 Ch. 7.3 - Prob. 13ST1 Ch. 7.3 - Prob. 14ST1 Ch. 7.3 - Prob. 15ST1 Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.4 - Prob. 1CE Ch. 7.4 - Prob. 2CE Ch. 7.4 - Prob. 3CE Ch. 7.4 - Prob. 4CE Ch. 7.4 - Prob. 5CE Ch. 7.4 - Prob. 6CE Ch. 7.4 - Prob. 7CE Ch. 7.4 - Prob. 8CE Ch. 7.4 - Prob. 9CE Ch. 7.4 - Prob. 10CE Ch. 7.4 - Prob. 11CE Ch. 7.4 - Prob. 12CE Ch. 7.4 - Prob. 13CE Ch. 7.4 - Prob. 1WE Ch. 7.4 - Prob. 2WE Ch. 7.4 - Prob. 3WE Ch. 7.4 - Prob. 4WE Ch. 7.4 - Prob. 5WE Ch. 7.4 - Prob. 6WE Ch. 7.4 - Prob. 7WE Ch. 7.4 - Prob. 8WE Ch. 7.4 - Prob. 9WE Ch. 7.4 - Prob. 10WE Ch. 7.4 - Prob. 11WE Ch. 7.4 - Prob. 12WE Ch. 7.4 - Prob. 13WE Ch. 7.4 - Prob. 14WE Ch. 7.4 - Prob. 15WE Ch. 7.4 - Prob. 16WE Ch. 7.4 - Prob. 17WE Ch. 7.4 - Prob. 18WE Ch. 7.4 - Prob. 19WE Ch. 7.4 - Prob. 20WE Ch. 7.4 - Prob. 21WE Ch. 7.4 - Prob. 22WE Ch. 7.4 - Prob. 23WE Ch. 7.4 - Prob. 24WE Ch. 7.4 - Prob. 25WE Ch. 7.4 - Prob. 26WE Ch. 7.4 - Prob. 27WE Ch. 7.4 - Prob. 28WE Ch. 7.4 - Prob. 29WE Ch. 7.4 - Prob. 30WE Ch. 7.4 - Prob. 31WE Ch. 7.4 - Prob. 32WE Ch. 7.4 - Prob. 33WE Ch. 7.4 - Prob. 34WE Ch. 7.4 - Prob. 35WE Ch. 7.4 - Prob. 1C Ch. 7.4 - Prob. 2C Ch. 7.4 - Prob. 1AE Ch. 7.4 - Prob. 2AE Ch. 7.4 - Prob. 3AE Ch. 7.4 - Prob. 4AE Ch. 7.4 - Prob. 1BE Ch. 7.4 - Prob. 2BE Ch. 7.4 - Prob. 3BE Ch. 7.4 - Prob. 4BE Ch. 7.5 - Prob. 1CE Ch. 7.5 - Prob. 2CE Ch. 7.5 - Prob. 3CE Ch. 7.5 - Prob. 4CE Ch. 7.5 - Prob. 5CE Ch. 7.5 - Prob. 6CE Ch. 7.5 - Prob. 7CE Ch. 7.5 - Prob. 8CE Ch. 7.5 - Prob. 9CE Ch. 7.5 - Prob. 1WE Ch. 7.5 - Prob. 2WE Ch. 7.5 - Prob. 3WE Ch. 7.5 - Prob. 4WE Ch. 7.5 - Prob. 5WE Ch. 7.5 - Prob. 6WE Ch. 7.5 - Prob. 7WE Ch. 7.5 - Prob. 8WE Ch. 7.5 - Prob. 9WE Ch. 7.5 - Prob. 10WE Ch. 7.5 - Prob. 11WE Ch. 7.5 - Prob. 12WE Ch. 7.5 - Prob. 13WE Ch. 7.5 - Prob. 14WE Ch. 7.5 - Prob. 15WE Ch. 7.5 - Prob. 16WE Ch. 7.5 - Prob. 17WE Ch. 7.5 - Prob. 18WE Ch. 7.5 - Prob. 19WE Ch. 7.5 - Prob. 20WE Ch. 7.5 - Prob. 21WE Ch. 7.5 - Prob. 22WE Ch. 7.5 - Prob. 23WE Ch. 7.5 - Prob. 1MRE Ch. 7.5 - Prob. 2MRE Ch. 7.6 - Prob. 1CE Ch. 7.6 - Prob. 2CE Ch. 7.6 - Prob. 3CE Ch. 7.6 - Prob. 4CE Ch. 7.6 - Prob. 5CE Ch. 7.6 - Prob. 6CE Ch. 7.6 - Prob. 7CE Ch. 7.6 - Prob. 8CE Ch. 7.6 - Prob. 9CE Ch. 7.6 - Prob. 1WE Ch. 7.6 - Prob. 2WE Ch. 7.6 - Prob. 3WE Ch. 7.6 - Prob. 4WE Ch. 7.6 - Prob. 5WE Ch. 7.6 - Prob. 6WE Ch. 7.6 - Prob. 7WE Ch. 7.6 - Prob. 8WE Ch. 7.6 - Prob. 9WE Ch. 7.6 - Prob. 10WE Ch. 7.6 - Prob. 11WE Ch. 7.6 - Prob. 12WE Ch. 7.6 - Prob. 13WE Ch. 7.6 - Prob. 14WE Ch. 7.6 - Prob. 15WE Ch. 7.6 - Prob. 16WE Ch. 7.6 - Prob. 17WE Ch. 7.6 - Prob. 18WE Ch. 7.6 - Prob. 19WE Ch. 7.6 - Prob. 20WE Ch. 7.6 - Prob. 21WE Ch. 7.6 - Prob. 22WE Ch. 7.6 - Prob. 23WE Ch. 7.6 - Prob. 24WE Ch. 7.6 - Prob. 25WE Ch. 7.6 - Prob. 26WE Ch. 7.6 - Prob. 27WE Ch. 7.6 - Prob. 28WE Ch. 7.6 - Prob. 29WE Ch. 7.6 - Prob. 30WE Ch. 7.6 - Prob. 31WE Ch. 7.6 - Prob. 32WE Ch. 7.6 - Prob. 33WE Ch. 7.6 - Prob. 1ST2 Ch. 7.6 - Prob. 2ST2 Ch. 7.6 - Prob. 3ST2 Ch. 7.6 - Prob. 4ST2 Ch. 7.6 - Prob. 5ST2 Ch. 7.6 - Prob. 6ST2 Ch. 7.6 - Prob. 7ST2 Ch. 7.6 - Prob. 8ST2 Ch. 7.6 - Prob. 9ST2 Ch. 7.6 - Prob. 10ST2 Ch. 7.6 - Prob. 11ST2 Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7 - Prob. 1CR Ch. 7 - Prob. 2CR Ch. 7 - Prob. 3CR Ch. 7 - Prob. 4CR Ch. 7 - Prob. 5CR Ch. 7 - Prob. 6CR Ch. 7 - Prob. 7CR Ch. 7 - Prob. 8CR Ch. 7 - Prob. 9CR Ch. 7 - Prob. 10CR Ch. 7 - Prob. 11CR Ch. 7 - Prob. 12CR Ch. 7 - Prob. 13CR Ch. 7 - Prob. 14CR Ch. 7 - Prob. 15CR Ch. 7 - Prob. 16CR Ch. 7 - Prob. 17CR Ch. 7 - Prob. 18CR Ch. 7 - Prob. 19CR Ch. 7 - Prob. 20CR Ch. 7 - Prob. 21CR Ch. 7 - Prob. 22CR Ch. 7 - Prob. 23CR Ch. 7 - Prob. 24CR Ch. 7 - Prob. 1CT Ch. 7 - Prob. 2CT Ch. 7 - Prob. 3CT Ch. 7 - Prob. 4CT Ch. 7 - Prob. 5CT Ch. 7 - Prob. 6CT Ch. 7 - Prob. 7CT Ch. 7 - Prob. 8CT Ch. 7 - Prob. 9CT Ch. 7 - Prob. 10CT Ch. 7 - Prob. 11CT Ch. 7 - Prob. 12CT Ch. 7 - Prob. 13CT Ch. 7 - Prob. 14CT Ch. 7 - Prob. 15CT Ch. 7 - Prob. 16CT Ch. 7 - Prob. 1AR Ch. 7 - Prob. 2AR Ch. 7 - Prob. 3AR Ch. 7 - Prob. 4AR Ch. 7 - Prob. 5AR Ch. 7 - Prob. 6AR Ch. 7 - Prob. 7AR Ch. 7 - Prob. 8AR Ch. 7 - Prob. 9AR Ch. 7 - Prob. 10AR Ch. 7 - Prob. 11AR Ch. 7 - Prob. 12AR Ch. 7 - Prob. 13AR Ch. 7 - Prob. 14AR Ch. 7 - Prob. 15AR Ch. 7 - Prob. 16AR Ch. 7 - Prob. 17AR Ch. 7 - Prob. 18AR Ch. 7 - Prob. 19AR Ch. 7 - Prob. 20AR Ch. 7 - Prob. 21AR Ch. 7 - Prob. 22AR Ch. 7 - Prob. 23AR Ch. 7 - Prob. 24AR Ch. 7 - Prob. 25AR Ch. 7 - Prob. 26AR Ch. 7 - Prob. 27AR Ch. 7 - Prob. 28AR Ch. 7 - Prob. 29AR Ch. 7 - Prob. 1CUR Ch. 7 - Prob. 2CUR Ch. 7 - Prob. 3CUR Ch. 7 - Prob. 4CUR Ch. 7 - Prob. 5CUR Ch. 7 - Prob. 6CUR Ch. 7 - Prob. 7CUR Ch. 7 - Prob. 8CUR Ch. 7 - Prob. 9CUR Ch. 7 - Prob. 10CUR Ch. 7 - Prob. 11CUR Ch. 7 - Prob. 1MCE Ch. 7 - Prob. 2MCE Ch. 7 - Prob. 3MCE Ch. 7 - Prob. 4MCE Ch. 7 - Prob. 5MCE Ch. 7 - Prob. 1ASNE Ch. 7 - Prob. 2ASNE Ch. 7 - Prob. 3ASNE Ch. 7 - Prob. 4ASNE Ch. 7 - Prob. 5ASNE Ch. 7 - Prob. 6ASNE Ch. 7 - Prob. 7ASNE Ch. 7 - Prob. 8ASNE Ch. 7 - Prob. 9ASNE Ch. 7 - Prob. 10ASNE Ch. 7 - Prob. 11ASNE Ch. 7 - Prob. 12ASNE Ch. 7 - Prob. 13ASNE Ch. 7 - Prob. 14ASNE Ch. 7 - Prob. 15ASNE Ch. 7 - Prob. 16ASNE Ch. 7 - Prob. 1CPE Ch. 7 - Prob. 2CPE Ch. 7 - Prob. 3CPE Ch. 7 - Prob. 4CPE Ch. 7 - Prob. 5CPE Ch. 7 - Prob. 6CPE Ch. 7 - Prob. 7CPE Ch. 7 - Prob. 8CPE Ch. 7 - Prob. 9CPE Ch. 7 - Prob. 1AE Ch. 7 - Prob. 2AE Ch. 7 - Prob. 3AE Ch. 7 - Prob. 4AE Ch. 7 - Prob. 5AE Ch. 7 - Prob. 6AE Ch. 7 - Prob. 7AE Ch. 7 - Prob. 8AE Ch. 7 - Prob. 9AE Ch. 7 - Prob. 10AE Ch. 7 - Prob. 11AE Ch. 7 - Prob. 12AE Ch. 7 - Prob. 13AE Ch. 7 - Prob. 14AE Ch. 7 - Prob. 15AE Ch. 7 - Prob. 1PE Ch. 7 - Prob. 2PE Ch. 7 - Prob. 3PE Ch. 7 - Prob. 4PE Ch. 7 - Prob. 5PE Ch. 7 - Prob. 6PE

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