Concept explainers
a.
Find
a.
Answer to Problem 40E
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
Consider the given sequence,
Now calculate the
b.
Identify the sequence of ratios are arithmetic, geometric or nothing.
b.
Answer to Problem 40E
Nothing.
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
Consider the ratio from table,
The sequence of ratios is not arithmetic nor geometric because there is no common difference.
c.
Plot the graph of terms found in part
c.
Answer to Problem 40E
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
The graph is as shown,
d.
Find the limit of sequence based on the graph.
d.
Answer to Problem 40E
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
The limit of the sequence is,
e.
Compare the value of golden ratio
e.
Answer to Problem 40E
The limit of the sequence is equal to golden ratio.
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
The value of golden ratio and limit of the sequence is, approximately same.
The limit of the sequence is equal to golden ratio.
f.
Research the term golden ratio.
f.
Answer to Problem 40E
The term golden ratio is the limit of the ratio successive terms of the Fibonacci sequence.
Explanation of Solution
Given information:
Fibonacci sequence
Calculation:
If the wall hanging is in rectangular shape and having length and breadth ratio is equal to
The term golden ratio is the limit of the ratio successive terms of the Fibonacci sequence.
Chapter 12 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (4th Edition)
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