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Math / Excursions in Modern Mathematics: Pearson New International Edition 8 / Chapter 13 / Problem 13

Excursions in Modern Mathematics: Pearson New International Edition | 8th Edition | ISBN: 9781292022048 | Authors: Peter Tannenbaum

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Consider the following sequence of equations involving Fibonacci numbers. 1 + 2 = 3 1 +

Chapter 13, Problem 13

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QUESTION:

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 f (a) Write down a reasonable choice for the fifth equation in this sequence. (b) Find the subscript that will make the following equation true. F1 + F3 + F5 + g+ F21 = F? (c) Find the subscript that will make the following equation true (assume N is odd). F1 + F3 + F5 + g+ FN = F?

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QUESTION:

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 f (a) Write down a reasonable choice for the fifth equation in this sequence. (b) Find the subscript that will make the following equation true. F1 + F3 + F5 + g+ F21 = F? (c) Find the subscript that will make the following equation true (assume N is odd). F1 + F3 + F5 + g+ FN = F?

ANSWER:

Step 1 of 3

The -th term of the given sequence is equal to the sum of the first Fibonacci's numbers with the odd index. Let's denote the given sequence with We would get:

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