Explanation Given information: Instruction to illustrates, two problems for the 4 th or 5 th grades involving the Fibonacci sequence and explain the solution in a way appropriate for that level. Calculation: First problem: Find the 9 th term in the Fibonacci sequence that starts with 1 and 1 as the first two terms. Let F 1 , F 2 , F 3 , F 4 , … , be the terms of the Fibonacci sequence. Here, F 1 = F 2 = 1 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. Thus, F n = F n − 1 + F n − 2 . By plugging n = 3 , F 3 = F 3 − 1 + F 3 − 2 = F 2 + F 1 = 1 + 1 = 2 , By plugging n = 4 , F 4 = F 4 − 1 + F 4 − 2 = F 3 + F 2 = 2 + 1 = 3 , By plugging n = 5 , F 5 = F 5 − 1 + F 5 − 2 = F 4 + F 3 = 3 + 2 = 5 . By plugging n = 6 , F 6 = F 6 − 1 + F 6 − 2 = F 5 + F 4 = 5 + 3 = 8 . By plugging n = 7 , F 7 = F 7 − 1 + F 7 − 2 = F 6 + F 5 = 8 + 5 = 13 . By plugging n = 8 , F 8 = F 8 − 1 + F 8 − 2 = F 7 + F 6 = 13 + 8 = 21 . By plugging n = 9 , F 9 = F 9 − 1 + F 9 − 2 = F 8 + F 7 = 21 + 13 = 34 . Therefore, the 9 th term in a Fibonacci sequence that starts with 1 and 1 as the first two terms is 34

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 10MC

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Chapter 1.2, Problem 9MC

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Two problems appropriate for the 4 th or 5 th grades involving the Fibonacci sequence and explain the solution in a way appropriate for that level.

Solution Summary: The author illustrates two problems appropriate for the 4 or 5 th grades involving the Fibonacci sequence.

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Two problems appropriate for the 4 th or 5 th grades involving the Fibonacci sequence and explain the solution in a way appropriate for that level.

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