# Python Program for Finding the n’th Multiple in Fibonacci Series

## Introduction

In this blog post, we will explore a Python program to find the n’th multiple of a given number in the Fibonacci series. The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones. By extending this series, we can create a sequence of multiples of a specified number.

## Problem Statement

Given a number `m`

and an index `n`

, we want to find the n’th multiple of `m`

in the Fibonacci series. For example, if `m`

is 3, and `n`

is 4, the program should find the 4th multiple of 3 in the Fibonacci series.

## Python Program

```
def fibonacci_multiple(m, n):
fib_series = [0, 1]
while len(fib_series) <= n:
fib_series.append(fib_series[-1] + fib_series[-2])
multiple_count = 0
index = 0
while multiple_count < n:
if fib_series[index] % m == 0:
multiple_count += 1
index += 1
return fib_series[index - 1]
# Example Usage
m_value = 3
n_value = 4
result = fibonacci_multiple(m_value, n_value)
print(f"The {n_value}th multiple of {m_value} in the Fibonacci series is: {result}")
```

## Program Explanation

We start by generating the Fibonacci series until its length becomes greater than or equal to

`n`

. We initialize the series with the first two elements, 0 and 1.We then iterate through the Fibonacci series to find the n’th multiple of the given number

`m`

. The`multiple_count`

variable keeps track of the multiples found, and the`index`

variable represents the current index in the series.The loop continues until we find the n’th multiple, and the result is the value at the found index in the Fibonacci series.

## Example Output

For the example with `m_value = 3`

and `n_value = 4`

, the output will be:

```
The 4th multiple of 3 in the Fibonacci series is: 21
```

## Concluded

This Python program efficiently finds the n’th multiple of a given number `m`

in the Fibonacci series. It showcases the use of the Fibonacci series generation and how to identify multiples within the series. Understanding such algorithms helps build a strong foundation for problem-solving in programming.

As an extension, readers can explore variations of this program, such as finding multiples in different sequences or optimizing the algorithm for large values of `n`

. Additionally, experimenting with different input values will enhance your understanding of the program’s behavior. Happy coding!

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