Friday, December 7

Fibonacci Series


Write a C program to generate the Fibonacci series.

Fibonacci series: Any number in the series is obtained by adding the previous two numbers of the series.
Let f(n) be n'th term.
f(0)=0;
f(1)=1;
f(n)=f(n-1)+f(n-2); (for n>=2)
Series is as follows
011
(1+0)
2 (1+1)
3 (1+2)
5 (2+3)
8 (3+5)
13 (5+8)
21 (8+13)
34 (13+21)
...and so on

Program: to generate Fibonacci Series(10 terms)

#include<stdio.h>
int main() 
{

int i, fib[25];                           //array fib stores numbers of Fibonacci series

fib[0] = 0;                              //initialized first element to 0

fib[1] = 1;                              //initialized second element to 1
for (i = 2; i < 10; i++)                //loop to generate ten elements
{

//i'th element of series is equal to the sum of i-1'th element and i-2'th element.

fib[i] = fib[i - 1] + fib[i - 2];

}
printf("The fibonacci series is as follows \n");

for (i = 0; i < 10; i++)                   //print all numbers in the series
{
printf("%d \n", fib[i]);
}
return 0;
}


Output:
The fibonacci series is as follows
01 1 2 3 5 8 13 21 34

Explanation:
The first two elements are initialized to 0, 1 respectively. Other elements in the series are generated by looping and adding previous two numbes. These numbers are stored in an array and ten elements of the series are printed as output.