Given that the 22st Fibonacci number is 17,711 use the golden ratio to find the 23rd Fibonacci number. Show you steps.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 57EQ
icon
Related questions
Question
Given that the 22st Fibonacci number is 17,711 use the golden ratio to find the 23rd Fibonacci number. Show you steps.
3. Consider the sequence of numbers defined by the recurrence relation
An = 4(an–1 – an-2),
2-1
with initial terms a1 =
2 and a2 = 4. Find az through a6. What pattern do
you see?
4. (a) Explain why 42
34 + 5 + 3 is not a valid way of expressing 42 as a sum of
non-consecutive Fibonacci numbers.
(b) Modify the sum from (a) to obtain a valid way.
5. Given that the 22st Fibonacci number is 17,711, use the Golden Ratio to find the 23rd
Fibonacci number.
6. Suppose a Golden Rectangle has its shorter side length equal to 5. What is the length
of the longer side? What is the area of the rectangle? (You may leave your answer in
terms of o.)
1
Rain to stop
DELL
Transcribed Image Text:3. Consider the sequence of numbers defined by the recurrence relation An = 4(an–1 – an-2), 2-1 with initial terms a1 = 2 and a2 = 4. Find az through a6. What pattern do you see? 4. (a) Explain why 42 34 + 5 + 3 is not a valid way of expressing 42 as a sum of non-consecutive Fibonacci numbers. (b) Modify the sum from (a) to obtain a valid way. 5. Given that the 22st Fibonacci number is 17,711, use the Golden Ratio to find the 23rd Fibonacci number. 6. Suppose a Golden Rectangle has its shorter side length equal to 5. What is the length of the longer side? What is the area of the rectangle? (You may leave your answer in terms of o.) 1 Rain to stop DELL
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage