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3. Consider the sequence of numbers defined by the recurrence relation An = 4(an-1 – an-2), with initial terms a1 = 2 and a2 = 4. Find az through a6. What pattern do you see?

3. Consider the sequence of numbers defined by the recurrence relation An = 4(an-1 – an-2), with initial terms a1 = 2 and a2 = 4. Find az through a6. What pattern do you see?

Algebra and Trigonometry (6th Edition)
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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Consider the sequence #3
1. If you have 12 boxes, then how many balls do you have to put randomly into the boxes in order to guarantee that some box will contain least 4 balls? 2. If you put 10 balls randomly into 12 boxes, is it guaranteed that no box will contain more than one ball? Why or why not? 3. Consider the sequence of numbers defined by the recurrence relation An 4(an-1 – an-2), || 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
Transcribed Image Text:1. If you have 12 boxes, then how many balls do you have to put randomly into the boxes in order to guarantee that some box will contain least 4 balls? 2. If you put 10 balls randomly into 12 boxes, is it guaranteed that no box will contain more than one ball? Why or why not? 3. Consider the sequence of numbers defined by the recurrence relation An 4(an-1 – an-2), || 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
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