   # Fibonacci Properties The Fibonacci sequence has many unusual properties. Experiment to decide which of the following properties are valid. Note: F n represents the n th Fibonacci number. a. 3 F n − F n − 2 = F n + 2 for n ≥ 3 b. F n F n + 3 = F n + 1 F n + 2 c. F 3 n is an even number. d. 5 F n − 2 F n − 2 = F n + 3 for n ≥ 3 ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 1.2, Problem 20ES
Textbook Problem
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## Fibonacci Properties The Fibonacci sequence has many unusual properties. Experiment to decide which of the following properties are valid. Note: F n represents the nth Fibonacci number.a. 3 F n − F n − 2 = F n + 2 for n ≥ 3 b. F n F n + 3 = F n + 1 F n + 2 c. F 3 n is an even number.d. 5 F n − 2 F n − 2 = F n + 3 for n ≥ 3

To determine

(a)

Determine 3FnFn2=Fn+2 for n3 is valid or not?

### Explanation of Solution

Given Information:

3FnFn2=Fn+2 for n3

Concept used:

Fibonacci series is the number which is sum of two preceding number.

Calculation:

Start with the right hand side, use nth-term formula to prove or disprove the above property,

Fn+2=Fn+21+Fn+</

To determine

(b)

The given property FnFn+3=Fn+1Fn+2 is valid or not.

To determine

(c)

F3n is an even number.

To determine

(d)

5Fn2Fn2=Fn+3 for n3

Is valid or not.

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