E. Answer the following problems.1. Determine whether each of the following statement about Fibonacci numbersis true or false. Show your solutions. Note: The first 10 terms of theFibonacci sequence are 1,1, 2,3, 5,8, 13, 21, 34, and 55.a. 2F, > Fn+1 for n 2 3b. 2F, + 4 = Fr+3 for n 2 32. A group of 266 persons consist of men, women and children. There are fourtimes as many men as children and twice as many women as children. Howmany of each are there? Use Polya's four-step problem solving strategy.3. In how many ways can you answer 12-question true-false test if you answereach question with either a "true" or a "false"? Use Polva's four-step problemsolving strategy.4. Use deductive reasoning to show that the following procedure alwaysproduces a number that is equal to the original number.Procedure: Pick a number. Multiply the number by 6 add 8. Divide the sum by2, subtract twice the original number, and subtract 4.5. Use deductive reasoning to show that the following procedure alwaysproduces the number 5.Procedure: Pick a number. Add 4 to the number and multiply the sum by 3.Subtract 7 and then decrease this difference by the triple of the originalnumber.

Name: E. Answer the following problems.1. Determine whether each of the fol
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Description: E. Answer the following problems.1. Determine whether each of the following statement about Fibonacci numbersis true or false. Show your solutions. Note: The first 10 terms of theFibonacci sequence are 1,1, 2,3, 5,8, 13, 21, 34, and 55.a. 2F, > Fn+1

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1. Determine whether each of the following statement about Fibonacci numbers is true or false. Show your solutions. Note: The first 10 terms of the Fibonacci sequence are 1,1, 2,3, 5, 8, 13, 21, 34, and 55. a. 2F, > Fn+1 for n 2 3 b. 2F, + 4 = Fn+3 for n 2 3

1. Determine whether each of the following statement about Fibonacci numbers is true or false. Show your solutions. Note: The first 10 terms of the Fibonacci sequence are 1,1, 2,3, 5, 8, 13, 21, 34, and 55. a. 2F, > Fn+1 for n 2 3 b. 2F, + 4 = Fn+3 for n 2 3

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

E. Answer the following problems.
1. Determine whether each of the following statement about Fibonacci numbers
is true or false. Show your solutions. Note: The first 10 terms of the
Fibonacci sequence are 1,1, 2,3, 5,8, 13, 21, 34, and 55.
a. 2F, > Fn+1 for n 2 3
b. 2F, + 4 = Fr+3 for n 2 3
2. A group of 266 persons consist of men, women and children. There are four
times as many men as children and twice as many women as children. How
many of each are there? Use Polya's four-step problem solving strategy.
3. In how many ways can you answer 12-question true-false test if you answer
each question with either a "true" or a "false"? Use Polva's four-step problem
solving strategy.
4. Use deductive reasoning to show that the following procedure always
produces a number that is equal to the original number.
Procedure: Pick a number. Multiply the number by 6 add 8. Divide the sum by
2, subtract twice the original number, and subtract 4.
5. Use deductive reasoning to show that the following procedure always
produces the number 5.
Procedure: Pick a number. Add 4 to the number and multiply the sum by 3.
Subtract 7 and then decrease this difference by the triple of the original
number.

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