Fibonacci sequence - calculating values

  • Thread starter Mokae
  • Start date
  • Tags
    Sequence
In summary, calculating Fibonacci sequences involves finding the sum of the previous two numbers in the series, starting with 1. There is also a constant called the golden ratio, denoted by the Greek letter "phi", that is used in the closed form expression for the terms in the sequence. If you have trouble understanding, asking your teacher or doing some research on Wikipedia can be helpful.
  • #1
Mokae
20
0
Hello,
a couple of days back I have learn about calculating fibonacci sequences but still I don;t quite uderstand the way it is calcilated, could you please give me some thoughts about it?

Thank you
 
Physics news on Phys.org
  • #2
it's easy
[tex] F_{n+1} = F_{n} + F_{n-1} [/tex]

So the next number in the series, [tex]F_{n+1}[/tex], is the sum of the previous two numbers

We start with 1. 1 plus the previous number, 0, is 1. 1+0=1. Now our series is 1,1
Now we take 1 and the number before it, 1 and add. 1+1=2. Now our series is 1,1,2
Now we take 2 and the previous number, 1, and add. 2+1=3. Now our series is 1,1,2,3.
Now take 3 and add the previous number, 2, and add. 3+2=5. 1,1,2,3,5
5+3=8, 8+5=13, 13+8=21, ... Fib Series looks like 1,1,2,3,5,8,13,21,...

got it?
 
Last edited:
  • #3
Thank you,
my profesor teach me to use sqrt of 2 plus 5 all divide 2
to calculate and i don't understand why. I am too scare to ask him again
 
  • #4
No, your teacher told you to use [itex]\frac{\sqrt{5}+1}{2}[/itex] to calculate Fibonnaci terms. That constant I just said is the golden ratio, commonly denoted by the greek letter "phi", [itex]\phi[/itex]. It is used in the closed form expression of the terms in the sequence. Don't be asked, you should ask him again.
 
  • #5

What is the Fibonacci sequence?

The Fibonacci sequence is a mathematical sequence where each number is the sum of the two preceding numbers, starting with 0 and 1. So, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.

How do you calculate the next value in the Fibonacci sequence?

To calculate the next value in the Fibonacci sequence, you simply add the two preceding numbers. For example, to find the 8th value in the sequence, you would add 3 and 5 to get 8.

What is the formula for the Fibonacci sequence?

The formula for the Fibonacci sequence is: Fn = Fn-1 + Fn-2, where the initial values are F0 = 0 and F1 = 1.

What is the significance of the Fibonacci sequence in nature?

The Fibonacci sequence can be found in many natural phenomena, such as the branching of trees, the arrangement of leaves on a stem, and the spiral pattern of seeds in a sunflower. This is because the sequence is a pattern of growth that is efficient and balanced, making it prevalent in nature.

How is the Fibonacci sequence used in computer algorithms?

The Fibonacci sequence is used in various computer algorithms, such as sorting and searching algorithms. It is also used in coding and encryption methods. Additionally, the sequence is used in programming languages to generate random numbers.

Similar threads

  • Calculus
2
Replies
36
Views
3K
  • Calculus
Replies
11
Views
1K
Replies
10
Views
2K
Replies
5
Views
1K
Replies
5
Views
2K
  • General Math
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
873
  • General Math
Replies
1
Views
1K
Back
Top