➤ FIBONACCI SERIES - The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, starting with 0 and 1. The series goes like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. Let's go through the process of solving the Fibonacci series step by step: 1. Define the Fibonacci series: The Fibonacci series is defined as follows: - F(0) = 0 - F(1) = 1 - F(n) = F(n-1) + F(n-2) for n >= 2 2. Determine the number of terms you want in the series: Decide how many terms of the Fibonacci series you want to generate. Let's say you want to generate the first 10 terms: F(0) to F(9). 3. Start with the base cases: The first two terms of the Fibonacci series are given: F(0) = 0 and F(1) = 1. 4. Calculate subsequent terms: Use the formula F(n) = F(n-1) + F(n-2) to calculate the next terms in the series. Start with n = 2 and keep calculating until you reach the desired number of terms. For example, to calculate F(2), we use the formula: F(2) = F(1) + F(0) = 1 + 0 = 1 To calculate F(3): F(3) = F(2) + F(1) = 1 + 1 = 2 Continue this process until you reach F(9) or the desired number of terms. 5. Write the series: Now that you have calculated all the terms, write down the Fibonacci series. For the first 10 terms, it will look like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 If you want to generate the Fibonacci series using a program, you can use the C program provided in the previous response. This program uses an iterative approach to calculate the series and displays the nth Fibonacci number as output. ➤ Program to Print Fibonacci series using C language. #include <stdio.h> int main() { int i, n; // initialize first and second terms int t1 = 0, t2 = 1; // initialize the next term (3rd term) int nextTerm = t1 + t2; // get no. of terms from user printf("Enter the number of terms: "); scanf("%d", &n); // print the first two terms t1 and t2 printf("Fibonacci Series: %d, %d, ", t1, t2); // print 3rd to nth terms for (i = 3; i <= n; ++i) { printf("%d, ", nextTerm); t1 = t2; t2 = nextTerm; nextTerm = t1 + t2; } return 0; } ➤ OUTPUT : Enter the number of terms: 8 Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, ➤ Program to Print Fibonacci series using Python language. def fibonacci(n): if n <= 0: return [] elif n == 1: return [0] elif n == 2: return [0, 1] else: fib_series = [0, 1] for i in range(2, n): #Here range start at 2 end with n inputs . next_term = fib_series[-1] + fib_series[-2] fib_series.append(next_term) return fib_series n = int(input("Enter the number of terms in the Fibonacci series: ")) #User place any number's fib_series = fibonacci(n) print("The Fibonacci series:") print(fib_series) ➤ OUTPUT : Enter the number of terms in the Fibonacci series: 8 The Fibonacci series: [0, 1, 1, 2, 3, 5, 8, 13]
Program To Generate Fibonacci Series.
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