Asked Dec 19, 2019
The Fibonacci sequence has many unusual properties. Experiment to decide which of the following properties are valid. Note: Fn represents the nth Fibonacci number.
5Fn − 2Fn − 2 = Fn + 3   for n ≥ 3
not valid    

Expert Answer

Step 1

Consider the given series known as Fibonacci sequence. Series starts with 0, 1 and then each next term is written as the summation of previous two terms.

Hence, the most common sequence becomes 0, 1, 1, 2, 3, 5, 8, 13, 21… on

Step 2

We will check it in two ways, first let’s do it in short way using a small value of ‘n’.



Image Transcriptionclose

5F, - 2F, = F+3 For n =3 5F, – 2F, = F, 5-1-2.0 =5 5-0 = 5 5 = 5 Hence, Valid.


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