The Fibonacci sequence is a sequence 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.

Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation
F_n = F_n-1 + F_n-2

In method 1, fibonacci series is generated upto 'n' number of terms, where n is entered by user

Whereas, in method 2, fibonacci series is generated upto a specific term. For example, if user enters 40, then, fibonacci series generated will be: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Next term 55 is not generated as it is greater than 40.

#include<stdio.h>
#include<conio.h>
void main()
{
   int i, n, t1, t2, next_term;

   printf("Enter the number of terms: ");
   scanf("%d", &n);

   printf("Fibonacci Series: ");

   t1 = 0;
   t2 = 1;
   for (i = 1; i <= n; i++)
   {
   		printf("%d, ", t1);
        next_term = t1 + t2;
        t1 = t2;
        t2 = next_term;
   }
   getch();
}

Enter the number of terms: 8
Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13,

#include<stdio.h>
#include<conio.h>
void main()
{
    int i, num, t1, t2, next_term;

    printf("Enter the number upto which Fibonacci series is to be displayed\t:");
    scanf("%d", &num);

    printf("Fibonacci Series: 0, 1, ");

    t1 = 0;
    t2 = 1;
    next_term = t1 + t2;
    while(next_term <= num)
    {
        printf("%d, ", next_term);
        t1 = t2;
        t2 = next_term;
        next_term = t1 + t2;
    }
    getch();
}

Enter the number upto which Fibonacci series is to be displayed :190
Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,