The following pattern is established involving terms of the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pat verify it. You may wish to refer to the first few terms of the sequence given in the text. 2²-1²=3 3²-1²=8 5²-2² =21 8²-3²=55 C... Each equation is the difference of the squares of two Fibonacci numbers. Each side of the next equation will equal 144. Following the pattern, write the next equation. The next equation in the list is written as (Do not evaluate. Use integers for any numbers in the expression.)
The following pattern is established involving terms of the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pat verify it. You may wish to refer to the first few terms of the sequence given in the text. 2²-1²=3 3²-1²=8 5²-2² =21 8²-3²=55 C... Each equation is the difference of the squares of two Fibonacci numbers. Each side of the next equation will equal 144. Following the pattern, write the next equation. The next equation in the list is written as (Do not evaluate. Use integers for any numbers in the expression.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.9: Geometric Sequences As Exponential Functions
Problem 3GP
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![The following pattern is established involving terms of the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pattern, and
verify it. You may wish to refer to the first few terms of the sequence given in the text.
2²-1²=3
3²-12 = 8
5²-2² =21
8²-3²=55
~
Each equation is the difference of the squares of two Fibonacci numbers. Each side of the next equation will equal 144.
Following the pattern, write the next equation.
The next equation in the list is written as
(Do not evaluate. Use integers for any numbers in the expression.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F382bdb49-1f2e-44fb-852b-c882649760f8%2F238e898f-1336-4f8c-b40f-66abb1c08b3a%2Fzjfpk0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following pattern is established involving terms of the Fibonacci sequence. Use inductive reasoning to make a conjecture concerning the next equation in the pattern, and
verify it. You may wish to refer to the first few terms of the sequence given in the text.
2²-1²=3
3²-12 = 8
5²-2² =21
8²-3²=55
~
Each equation is the difference of the squares of two Fibonacci numbers. Each side of the next equation will equal 144.
Following the pattern, write the next equation.
The next equation in the list is written as
(Do not evaluate. Use integers for any numbers in the expression.)
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