Ch 9 Practice Problems

Ch 9 Practice Problems - 8 Use the following recursive...

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1 Math 110 Chapter 9 Practice Problems Here are some problems for you to try from Chapter 9. Use your book or notes from class to help find the answers. 1. Describe the Fibonacci Sequence by listing the first 15 terms and explain how the sequence progresses. 2. The first two Fibonacci numbers (called seeds) are 1 and 1. What would be the first 10 numbers of the sequence that uses the recursive rule for the Fibonacci numbers but starts with seeds of 1 and 3? What is this sequence of numbers known as? 3. If F 36 14 930 352 = , , and F 37 24 157 817 = , , , find a) F 38 b) F 39 4. If F 31 1 346 269 = , , and F 33 3 524 578 = , , , find a) F 32 b) F 34 5. Consider the following sequence of equations involving Fibonacci numbers. 1 + 2 = 3 1 + 2 + 5 = 8 1 + 2 + 5 + 13 = 21 1 + 2 + 5 + 13 + 34 = 55 Write down what you think is the fifth equation in this sequence. 6. What do Jacques Binet and Leonard Euler have to do with Fibonacci? 7. What is the difference between a Recursive definition and an Explicit definition?

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Unformatted text preview: 8. Use the following recursive rules to find the first seven numbers in the sequence. a. G 1 1 = and G 2 4 = b. H 1 2 = and H 2 5 = G G G N N N = ⋅--1 2 H H H N N N = +--1 2 2 9. Use the following explicit rules to find the 14 th number in the sequence. a. J N N =-5 4 b. Y N N N = + 2 2 10. What are the next three numbers in each sequence and describe how you determined these values. . a. 5, 9, 13, 17, 21, . .. b. 1, 8, 27, 64, 125, . .. 11. What is the Golden Ratio? What is its EXACT representation? What is its APPROXIMATE value? 12. How is the Golden Ratio related to Fibonacci numbers? 13. What are other names for the Golden Ratio? 14. What is a golden rectangle? 15. What is a Fibonacci rectangle? Draw and label the sides of three different Fibonacci rectangles. 16. Give some examples of gnomonic growth in nature....
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This note was uploaded on 05/06/2008 for the course MATH 110 taught by Professor Pietro during the Spring '08 term at SUNY Fredonia.

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Ch 9 Practice Problems - 8 Use the following recursive...

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