d. Using the squared Fibonacci numbers, find the sum of the 1st and the 2nd terms, then the sum of the 1st, 2nd, and the 3rd terms, next the sum of the 1st, 2nd, 3rd, and the 4th terms, continue adding the square of the Fibonacci numbers up to the 6th term. e. What do you observe about the sum? f. Are the sum shows Fibonacci numbers? Why? g. Form two Fibonacci numbers from the sum found in letter D
d. Using the squared Fibonacci numbers, find the sum of the 1st and the 2nd terms, then the sum of the 1st, 2nd, and the 3rd terms, next the sum of the 1st, 2nd, 3rd, and the 4th terms, continue adding the square of the Fibonacci numbers up to the 6th term. e. What do you observe about the sum? f. Are the sum shows Fibonacci numbers? Why? g. Form two Fibonacci numbers from the sum found in letter D
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.6: The Pythagorean Theorem
Problem 3CE
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![Investigate the relationship of Fibonacci numbers with the Golder ratio.
1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
a. Find the square of the given Fibonacci numbers above.
b. Add two successive terms of the squared Fibonacci numbers above starting from
the first term and the second. Then the second and the third, next the third and
the fourth, and so on. For uniformity, do this up to the sixth and the seventh terms
only.
c.
What do you observe about the sum?
d. Using the squared Fibonacci numbers, find the sum of the 1st and the 2nd terms,
then the sum of the 1st, 2nd, and the 3rd terms, next the sum of the 1st, 2nd, 3rd,
and the 4th terms, continue adding the square of the Fibonacci numbers up to
the 6th term.
e. What do you observe about the sum?
f. Are the sum shows Fibonacci numbers? Why?
g. Form two Fibonacci numbers from the sum found in letter D
Answer
only
D, E, F & G](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa876f0ef-bb5d-4c75-a8d5-4baaa8ac3f10%2F20acadca-6907-4be0-aac9-49064d123328%2Ff92fmke_processed.png&w=3840&q=75)
Transcribed Image Text:Investigate the relationship of Fibonacci numbers with the Golder ratio.
1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
a. Find the square of the given Fibonacci numbers above.
b. Add two successive terms of the squared Fibonacci numbers above starting from
the first term and the second. Then the second and the third, next the third and
the fourth, and so on. For uniformity, do this up to the sixth and the seventh terms
only.
c.
What do you observe about the sum?
d. Using the squared Fibonacci numbers, find the sum of the 1st and the 2nd terms,
then the sum of the 1st, 2nd, and the 3rd terms, next the sum of the 1st, 2nd, 3rd,
and the 4th terms, continue adding the square of the Fibonacci numbers up to
the 6th term.
e. What do you observe about the sum?
f. Are the sum shows Fibonacci numbers? Why?
g. Form two Fibonacci numbers from the sum found in letter D
Answer
only
D, E, F & G
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