13. Fibonacci and Lucas numbers a.) Given four consecutive Fibonacci numbers (this means four Fibonacci numbers in a row, for example, 1, 1, 2, 3) if you square the middle two and then subtract the smaller result from the larger result, the result is equal to the smallest and largest of all four Fibonacci numbers. Fill in the blank and show several examples that fit this pattern. of the Understand the problem: Given four consecutive Fibonacci numbers → 1, 1, 2, 3 square the middle two → 1, 12, 2?, 3 write the squares and then subtract the smaller result from the larger result → 4–1 = 3 look at the smallest and largest in the sequence 1, 1, 2, 3 versus the answer of 3. What can you do to 1 and 3 to get 3? 1 3 = 3 Another example: Given four consecutive Fibonacci numbers → 2, 3, 5, 8 square the middle two → 2, 3², 5², 8 Fill in the answers: and then subtract the smaller result from the larger result. Fill in the answers: the result is equal to the, how they relate to your answer and describe in words. of the smallest and largest → look at 2 and 8 and see Your own example:

13. Fibonacci and Lucas numbers a.) Given four consecutive Fibonacci numbers (this means four Fibonacci numbers in a row, for example, 1, 1, 2, 3) if you square the middle two and then subtract the smaller result from the larger result, the result is equal to the smallest and largest of all four Fibonacci numbers. Fill in the blank and show several examples that fit this pattern. of the Understand the problem: Given four consecutive Fibonacci numbers → 1, 1, 2, 3 square the middle two → 1, 12, 2?, 3 write the squares and then subtract the smaller result from the larger result → 4–1 = 3 look at the smallest and largest in the sequence 1, 1, 2, 3 versus the answer of 3. What can you do to 1 and 3 to get 3? 1 3 = 3 Another example: Given four consecutive Fibonacci numbers → 2, 3, 5, 8 square the middle two → 2, 3², 5², 8 Fill in the answers: and then subtract the smaller result from the larger result. Fill in the answers: the result is equal to the, how they relate to your answer and describe in words. of the smallest and largest → look at 2 and 8 and see Your own example:

Name: Project 2: Number Patterns, p. 1913. Fibonacci and Lucas numbersa.) G
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Description: Project 2: Number Patterns, p. 1913. Fibonacci and Lucas numbersa.) Given four consecutive Fibonacci numbers (this means four Fibonacci numbers in arow, for example, 1, 1, 2, 3) if you square the middle two and then subtract thesmaller result from t

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Project 2: Number Patterns, p. 19
13. Fibonacci and Lucas numbers
a.) Given four consecutive Fibonacci numbers (this means four Fibonacci numbers in a
row, for example, 1, 1, 2, 3) if you square the middle two and then subtract the
smaller result from the larger result, the result is equal to the
smallest and largest of all four Fibonacci numbers. Fill in the blank and show
several examples that fit this pattern.
of the
Understand the problem:
Given four consecutive Fibonacci numbers → 1, 1, 2, 3
square the middle two –→
1, 12, 22, 3
write the squares
and then subtract the smaller result from the larger result → 4–1 = 3
look at the smallest and largest in the sequence 1, 1, 2, 3 versus the answer of 3.
What can you do to 1 and 3 to get 3? 1
3 = 3
Another example:
Given four consecutive Fibonacci numbers 2, 3, 5, 8
square the middle two → 2, 3², 5², 8
Fill in the answers:
and then subtract the smaller result from the larger result.
Fill in the answers:
the result is equal to the
how they relate to your answer and describe in words.
of the smallest and largest → look at 2 and 8 and see
Your own example:
b.) Another sequence that is constructed in a similar way to the Fibonacci sequence is
the Lucas Sequence: 1, 3, 4, 7, 11, 18, 29, 47, 76, 123,
Find the next two numbers in the Lucas sequence.
c.) If you take four consecutive Lucas numbers, square the middle two and then
subtract the smaller result from the larger result, do you get the
smallest and largest, the same way as the Fibonacci sequence? Show several
examples, then state your conclusion.
of the

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