Solution to 3Fn − Fn−2 = Fn+2, for n ≥ 3. - Sikademy
Author Image

Archangel Macsika

3Fn − Fn−2 = Fn+2, for n ≥ 3.

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

The sequence of Fibonacci numbers, F_0, F_1, F_2,F_3, . . ., are defined by the following equations: 


F_0=0,F_1=1,F_n=F_{n-1}+F_{n-2}, n\geq 2

Then for n\geq 3

F_{n+2}=F_{n+1}+F_n=F_n+F_{n-1}+F_n

=2F_n+F_n-F_{n-2}=3F_n-F_{n-2}

Therefore


3F_n-F_{n-2}=F_{n+2}, n\geq 3

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-611-qpid-496