Fibonacci Series In Python

# Python Program to Print the Fibonacci sequence

In this program, you’ll learn to print the Fibonacci sequence using a while loop.

To understand this example, you should have knowledge of the following Python programming topics:

- Python if…else Statement
- Python while Loop

A Fibonacci sequence is the integer sequence of 0, 1, 1, 2, 3, 5, 8….

The first two terms are 0 and 1. All other terms are obtained by adding the preceding two terms. This means to say the nth term is the sum of (n-1)th and (n-2)th term.

## Source Code

```
# Program to display the Fibonacci sequence up to n-th term
nterms = int(input("How many terms? "))
# first two terms
n1, n2 = 0, 1
count = 0
# check if the number of terms is valid
if nterms <= 0:
print("Please enter a positive integer")
elif nterms == 1:
print("Fibonacci sequence upto",nterms,":")
print(n1)
else:
print("Fibonacci sequence:")
while count < nterms:
print(n1)
nth = n1 + n2
# update values
n1 = n2
n2 = nth
count += 1
```

**Output**

How many terms? 7 Fibonacci sequence: 0 1 1 2 3 5 8

Here, we store the number of terms in `nterms`. We initialize the first term to 0 and the second term to 1.

If the number of terms is more than 2, we use a `while`

loop to find the next term in the sequence by adding the preceding two terms. We then interchange the variables (update it) and continue on with the process.

You can also solve this problem using recursion: Python program to print the Fibonacci sequence using recursion.

The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

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

with seed values

F_{0}= 0 and F_{1}= 1.

**Method 1 ( Use recursion ) :**

- Python

`# Function for nth Fibonacci number` `def` `Fibonacci(n):` `# Check if input is 0 then it will` `# print incorrect input` `if` `n < ` `0` `:` `print` `(` `"Incorrect input"` `)` `# Check if n is 0` `# then it will return 0` `elif` `n ` `=` `=` `0` `:` `return` `0` `# Check if n is 1,2` `# it will return 1` `elif` `n ` `=` `=` `1` `or` `n ` `=` `=` `2` `:` `return` `1` `else` `:` `return` `Fibonacci(n` `-` `1` `) ` `+` `Fibonacci(n` `-` `2` `)` `# Driver Program` `print` `(Fibonacci(` `9` `))` `# This code is contributed by Saket Modi` `# then corrected and improved by Himanshu Kanojiya` |

**Output**

34

**Method 2 ( Use Dynamic Programming ) :**

`# Function for nth fibonacci` `# number - Dynamic Programing` `# Taking 1st two fibonacci nubers as 0 and 1` `FibArray ` `=` `[` `0` `, ` `1` `]` `def` `fibonacci(n):` `# Check is n is less` `# than 0` `if` `n <` `=` `0` `:` `print` `(` `"Incorrect input"` `)` `# Check is n is less` `# than len(FibArray)` `elif` `n <` `=` `len` `(FibArray):` `return` `FibArray[n ` `-` `1` `]` `else` `:` `temp_fib ` `=` `fibonacci(n ` `-` `1` `) ` `+` `fibonacci(n ` `-` `2` `)` `FibArray.append(temp_fib)` `return` `temp_fib` `# Driver Program` `print` `(fibonacci(` `9` `))` `# This code is contributed by Saket Modi` |

**Output**

21

**Method 3 ( Space Optimized):**

- Python

`# Function for nth fibonacci` `# number - Space Optimisataion` `# Taking 1st two fibonacci numbers as 0 and 1` `def` `fibonacci(n):` `a ` `=` `0` `b ` `=` `1` `# Check is n is less` `# than 0` `if` `n < ` `0` `:` `print` `(` `"Incorrect input"` `)` `# Check is n is equal` `# to 0` `elif` `n ` `=` `=` `0` `:` `return` `0` `# Check if n is equal to 1` `elif` `n ` `=` `=` `1` `:` `return` `b` `else` `:` `for` `i ` `in` `range` `(` `1` `, n):` `c ` `=` `a ` `+` `b` `a ` `=` `b` `b ` `=` `c` `return` `b` `# Driver Program` `print` `(fibonacci(` `9` `))` `# This code is contributed by Saket Modi` `# Then corrected and improved by Himanshu Kanojiya` |

**Output**

34

Please refer complete article on Program for Fibonacci numbers for more details!

### How do you do the Fibonacci series in Python?

- INPUT FORMAT: Input consists of an integer.
- OUTPUT FORMAT: …
- SAMPLE INPUT: 7.
- SAMPLE OUTPUT: 0 1 1 2 3 5 8.
- PREREQUISITE KNOWLEDGE: while loop in
**Python**and Recursion in**Python**. … - Step 1:Input the ‘n’ value until which the
**Fibonacci series**has to be generated. - Step 3:while (count <= n)
- Step 5:Increment the count variable.

### How do you find the nth Fibonacci number in Python?

**Solution Review : Compute nth Fibonacci Number**

- def
**fibonacci**(n): - if n <= 1:
- return n.
- else:
- return(
**fibonacci**(n-1) +**fibonacci**(n-2)) - print(
**Fibonacci**(4))

**What is the Fibonacci Series formula?**

_{n}= F

_{n}

_{–}

_{1}+ F

_{n}

_{–}

_{2}. to get the rest. Thus the

**sequence**begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … This

**sequence**of

**Fibonacci numbers**arises all over mathematics and also in nature.

**What is the logic of the Fibonacci series?**

**Fibonacci Series**is a pattern of

**numbers**where each number is the result of the addition of the previous two consecutive

**numbers**. The first 2

**numbers**start with 0 and 1. The third

**numbers**in the

**sequence**are 0+1=1. The 4th number is the addition of the 2nd and 3rd number i.e. 1+1=2 and so on.

**Is 0 a Fibonacci number?**

**Fibonacci sequence**is a

**series**of

**numbers**where a

**number**is the addition of the last two

**numbers**, starting with

**0**, and 1. The

**Fibonacci Sequence**:

**0**, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

### How do you create Fibonacci numbers?

**Fibonacci Sequence**is the

**series**of

**numbers**: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

…

**The next number is found by adding up the two numbers before it:**

- the 2 is found by adding the two
**numbers**before it (1+1), - the 3 is found by adding the two
**numbers**before it (1+2), - the 5 is (2+3),
- and so on!

**What is nth Fibonacci number?**

**nth Fibonacci number**in terms of the two before it: the n-th

**Fibonacci number**is the sum of the (n-1)th and the (n-2)th.

### What is the use of the Fibonacci series?

**Fibonacci numbers**are used to create technical indicators using a mathematical

**sequence**developed by the Italian mathematician, commonly referred to as “

**Fibonacci**,” in the 13th century. The

**sequence**of

**numbers**, starting with zero and one, is created by adding the previous two

**numbers**.

### How do you find a number that is Fibonacci or not?

**check**if a

**number**if a

**Fibonacci number**or

**not**, is as below: N is a

**Fibonacci number**if and only if ( 5*N

^{2}+ 4 ) or ( 5*N

^{2}– 4 ) is a perfect square! For Example, 3 is a

**Fibonacci number**since (5*3*3 + 4) is 49 which is 7*7.

### What is the biggest Fibonacci number?

3340367

### How do you use the Fibonacci **equation?**

This will give you the second number in the sequence. Remember, to find any given number in the **Fibonacci** sequence, you simply add the two previous numbers in the sequence. To create the sequence, you should think of 0 coming before 1 (the first term), so 1 + 0 = 1.

### What does Fibonacci mean in English?

**is**the sum of the two immediately preceding. See the full

**definition**.

### What is Fibonacci in Java?

**Fibonacci**series is a series where the next term is the sum of the previous two terms. The first two terms of the

**Fibonacci**sequence are 0 followed by 1. The

**Fibonacci**sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, …

### What are Fibonacci ratios?

**Fibonacci**numbers. Each level is associated with a percentage. The percentage is how much of a prior move the price has retraced. The

**Fibonacci retracement**levels are 23.6%, 38.2%, 61.8%, and 78.6%. While not officially a

**Fibonacci ratio**, 50% is also used.

### How does Fibonacci recursion work?

**Recursion**will happen till the bottom of each branch in the tree structure is reached with the resulting value of 1 or 0. During

**recursion**these 1’s and 0’s are added till the value of the

**Fibonacci**number is calculated and returned to the code called the

**Fibonacci**method in the first place.

### What is Fibonacci series in C++?

**Fibonacci sequence**is a

**series**where the next term is the sum of the previous two terms. The first two terms of the

**Fibonacci sequence**is 0 followed by 1. The

**Fibonacci sequence**: 0, 1, 1, 2, 3, 5, 8, 13, 21.

### How did Leonardo Fibonacci discover the Fibonacci sequence?

**sequence**progressed by adding the previous two terms (in mathematical terms, F

_{n}= F

_{n}

_{–}

_{1}+ F

_{n}

_{–}

_{2}), a

**sequence**which could, in theory, extend indefinitely.

### Is the Fibonacci sequence infinite?

**infinite number**of

**Fibonacci**numbers with any given

**number**as a factor!

### What is the golden ratio in Fibonacci?

**golden ratio**is about 1.618, and represented by the Greek letter

**phi**, Φ. The

**golden ratio**is best approximated by the famous “

**Fibonacci**numbers.”

**Fibonacci**numbers are a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers.