Fibonacci Sequence Formula
Fibonacci formula is used to find the nth term of the sequence when its first and second terms are given.
The nth term of the Fibonacci Sequence is represented as Fn. It is given by the following recursive formula,
Fn = Fn-1 + Fn-2
where,
- n > 1
- First term is 0 i.e., F0 = 0
- Second term is 1 i.e., F1 = 1
Using this formula, we can easily find the various terms of the Fibonacci Sequence. Suppose we have to find the 3rd term of this Sequence then we would require the 2nd and the 1st term according to the given formula, then the 3rd term is calculated as,
- F3 = F2 + F1 = 1 + 0 = 1
Thus, the third term in the Fibonacci Sequence is 1, and similarly, the next terms of the sequence can also be found as,
- F4 = F3 + F2 = 1 + 1 = 2
- F5 = F4 + F3 = 2 + 1 = 3
and so on.
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List of Fibonacci sequence
Below is the first 20 Fibonacci Sequence List.
|
Terms of Fibonacci Sequence |
|
|---|---|
| F0 = 0 | F10 = 45 |
| F1 = 1 | F11 = 89 |
| F2 = 1 | F12 = 134 |
| F3 = 2 | F13 = 223 |
| F4 = 3 | F14 = 377 |
| F5 = 5 | F15 = 610 |
| F6 = 8 | F16 = 987 |
| F7 = 13 | F17 = 1597 |
| F8 = 21 | F18 = 2584 |
| F9 = 34 | F19 = 4181 |
- Fibonacci Sequences have infinite terms.
- By closely observing the table we can say that Fn = Fn-1 + Fn-2 for every n > 1.
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Fibonacci Sequence: Definition, Formula, List and Examples
Fibonacci sequence is a series of numbers where each number is the sum of the two numbers that come before it. The numbers in the Fibonacci sequence are known as Fibonacci numbers and are usually represented by the symbol Fₙ. Fibonacci sequence numbers start with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
Fibonacci Sequence
Table of Content
- Fibonacci Sequence
- Fibonacci Sequence Formula
- Fibonacci Spiral
- Golden Ratio to find Fibonacci Sequence
- Golden Ratio Formula
- Fibonacci Series in Pascal’s Triangle
- Fibonacci Sequence Properties
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence
- Fibonacci Sequence – FAQs
There are various applications of Fibonacci sequence in real life, such as in the growth of trees. As the tree grows, the trunk grows and spirals outward. The branches also follow the Fibonacci sequence, starting with one trunk that splits into two, then one of those branches splits into two, and so on.
Let’s learn about Fibonacci Sequence in detail, including Fibonacci sequence formula, properties, and examples.