Explanation Given information: The first two terms of the sequence are any numbers. The sequence follows the pattern of a Fibonacci type sequence. Calculation: Let x and y are the first two terms of the sequence. The sequence follows the pattern of a Fibonacci type sequence. In a Fibonacci sequence the first two terms are arbitrary and every term starting from the third is the sum of the two previous terms. Starting with x and y as the first two terms of the Fibonacci sequence. Let F 1 , F 2 , F 3 , F 4 , … , be the terms of the Fibonacci sequence. Therefore, F 1 = x , F 2 = y , F 3 = x + y , F 4 = x + 2 y , F 5 = 2 x + 3 y , … Take x = 2 , y = 3 F 1 = 2 , F 2 = 3 , F 3 = 5 , F 4 = 8 , F 5 = 13 , … Thus, the Fibonacci sequence is 2 , 3 , 5 , 8 , 13 , … Take x = 1 , y = 2 F 1 = 1 , F 2 = 2 , F 3 = 3 , F 4 = 5 , F 5 = 8 , … Thus, the Fibonacci sequence is 1 , 2 , 3 , 5 , 8 , … Take x = 3 , y = 2 F 1 = 3 , F 2 = 2 , F 3 = 5 , F 4 = 7 , F 5 = 12 , … Thus, the Fibonacci sequence is 3 , 2 , 5 , 7 , 12 , … Take some Fibonacci sequences are 2 , 3 , 5 , 8 , 13 , … , 1 , 2 , 3 , 5 , 8 , … and 3 , 2 , 5 , 7 , 12 , … . Starting with 1 and 1 as the first two terms of the Fibonacci sequence. Here, F 1 = F 2 = 1 and F n = F n − 1 + F n − 2 . The sum of the n odd terms of the sequence is equal to twice the number of terms of the sequence

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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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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Chapter 1.2, Problem 9MC

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Whether a sequence that follows the same pattern as the Fibonacci sequence, but in which the first two terms are any numbers, is a Fibonacci type sequence, and compare their behavior with the Fibonacci sequence.

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Chapter 1.2, Problem 8MC

Chapter 1.2, Problem 10MC

Chapter 1 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

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Whether a sequence that follows the same pattern as the Fibonacci sequence, but in which the first two terms are any numbers, is a Fibonacci type sequence, and compare their behavior with the Fibonacci sequence.

Solution Summary: The author explains that a sequence that follows the same pattern as the Fibonacci sequence, but in which the first two terms are any numbers, isn't arbitrary and every term starting from the third is the sum of

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Whether a sequence that follows the same pattern as the Fibonacci sequence, but in which the first two terms are any numbers, is a Fibonacci type sequence, and compare their behavior with the Fibonacci sequence.

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Chapter 1 Solutions