Q 4: Analyze and write a program to display series: 0 1 1 2 3 5 8 13 21 34 55 89.

The Fibonacci sequence is a series where the next term is the sum of pervious two terms. The first two terms of the Fibonacci sequence is 0 followed by 1.

By definition the first two numbers are:

 

Fibonacci(0) = 0 =>t1

Fibonacci(1) = 1 =>t2

 

The next number is always the sum of the previous two. Fibonacci(n) = Fibonacci(n-1) + Fibonacci(n-2)

 

Fibonacci(2) = 0 + 1 = 1   => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(3) = 1 + 1 = 2 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(4) = 1 + 2 = 3 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(5) = 2 + 3 = 5 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(6) = 3 + 5 = 8 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(7) = 5 + 8 = 13 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(8) = 8 + 13 = 21 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(9) = 13 + 21 = 34 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(10) = 21 + 34 = 55 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

Fibonacci(11) = 34 + 55 = 89 => nextTerm =t1+t2; t1 = t2; t2 = nextTerm;

 

Program

#include <stdio.h>

void main()

{

    int i, n, t1 = 0, t2 = 1, nextTerm;

 

    printf("Enter the number of terms: ");

    scanf("%d", &n);

 

    printf("Fibonacci Series: ");

 

    for (i = 1; i <= n; i++)

    {

        printf("%d, ", t1);

        nextTerm = t1 + t2;

        t1 = t2;

        t2 = nextTerm;

    }

 }