What is the 30th term in the Fibonacci series?

We all know about the famous Fibonacci (was the name given to Leonardo Pisano) Series. In this series, each number is the sum of the two preceding ones, starting from 0 and 1. That is \(F_0\)=0 and \(F_1\)=1

and

\(F_n\)=\(F_{n−1}\)+\(F_{n−2}\) for n>1

In some old books \(F_0\) is omitted and the entire things starts with \(F_1\)and \(F_2\)that is \(F_1\)=\(F_2\)=1

so it starts like this 0,1,1,2,3,5,8,13,……..

But, is this really possible to find the 30th term in the Fibonacci series by just adding the previous terms in order to get such large terms?

Now, in order to find the 30th term of the above mentioned series we write a program in C and that is

1. #include <stdio.h>
2. Void main ()
3. {
4. long int i, n, t1 = 0, t2 = 1, nextTerm;
5. printf("Enter the number of terms: ");
6. scanf("%li", &n);
7. printf("Fibonacci Series: ");
8. for (i = 1; i <= n; ++i)
9. {
10. printf("%d, ", t1);
11. nextTerm = t1 + t2;
12. t1 = t2;
13. t2 = nextTerm;
14. }
15. }

After compiling the above program in C , we enter the value of ?n as 30 and the output is

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 5142290, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229

Here 514229 is the 30th term of the Fibonacci Series.

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• Arnold's Cat Mapping
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