# Data Structure & Algorithms Fibonacci Series

Fibonacci series generates the subsequent number by adding two previous numbers. Fibonacci series starts from two numbers − F0 & F1. The initial values of F0 & F1 can be taken 0, 1 or 1, 1 respectively.

Fibonacci series satisfies the following conditions −

```Fn = Fn-1 + Fn-2
```

Hence, a Fibonacci series can look like this −

F8 = 0 1 1 2 3 5 8 13

or, this −

F8 = 1 1 2 3 5 8 13 21

For illustration purpose, Fibonacci of F8 is displayed as − ## Fibonacci Iterative Algorithm

First we try to draft the iterative algorithm for Fibonacci series.

```Procedure Fibonacci(n)
declare f0, f1, fib, loop

set f0 to 0
set f1 to 1

<b>display f0, f1</b>

for loop ← 1 to n

fib ← f0 + f1
f0 ← f1
f1 ← fib

<b>display fib</b>
end for

end procedure
```

## Fibonacci Recursive Algorithm

Let us learn how to create a recursive algorithm Fibonacci series. The base criteria of recursion.

```START
Procedure Fibonacci(n)
declare f0, f1, fib, loop

set f0 to 0
set f1 to 1

display f0, f1

for loop ← 1 to n

fib ← f0 + f1
f0 ← f1
f1 ← fib

display fib
end for

END
```

To see the implementation of above algorithm in c programming language, click here.