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. 1 = 1 1+2=3 1+2+5=8 1+2+5+13= 21 1+2+5+13+ 34 = 55 Each equation skips the next Fibonacci number to add the one after. 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=0 (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 pattern, and verify it. You may wish to refer to the first few terms of the sequence given in the text. 1 = 1 1+2=3 1+2+5=8 1+2+5+13= 21 1+2+5+13+ 34 = 55 Each equation skips the next Fibonacci number to add the one after. 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=0 (Do not evaluate. Use integers for any numbers in the expression.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
1 = 1
1+2=3
1+2+5=8
1+2+5+13=21
1+2+5+13+34 = 55
Each equation skips the next Fibonacci number to add the one after. 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=0
(Do not evaluate. Use integers for any numbers in the expression.)
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