Posted on by Kalkicode
Code Mathematics

Average of first n natural numbers

Calculating the average of the first n natural numbers is a basic mathematical problem that involves finding the sum of the first n integers and then dividing that sum by n. This problem showcases how a simple mathematical formula can be used to find meaningful results.

Problem Statement

Given a positive integer n, the problem is to find the average of the first n natural numbers.

Idea to Solve the Problem

The sum of the first n natural numbers can be expressed using the well-known formula: 1 + 2 + 3 + ... + n. The formula for the sum of the first n natural numbers is given by:

Sum = 1 + 2 + 3 + ... + n = (n * (n + 1)) / 2

The average of these numbers can be calculated by dividing the sum by n.

Pseudocode

function findAverage(n)
    if n <= 0
        return
    
    sum = (n * (n + 1)) / 2
    average = sum / n
    
    print average

Algorithm Explanation

  1. The findAverage function takes a positive integer n as input.

  2. If n is less than or equal to 0, the function returns immediately to handle invalid inputs.

  3. Calculate the sum of the first n natural numbers using the formula (n * (n + 1)) / 2.

  4. Calculate the average by dividing the sum by n.

  5. Print the calculated average.

Program Solution

// C Program
// Average of first n natural numbers
#include <stdio.h>

void findAverage(int n)
{
	if (n <= 0)
	{
		return;
	}
	// Calculate sum of n natural number
  	// Formula = (n × (n + 1)) / 2.0
	double sum = (n * (n + 1)) / 2.0;
	// Calculate Average
	double average = sum / n;
	// Display calculated result
	printf("\n %lf", average);
}
int main()
{
	int n = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 

	*/
	findAverage(n);
	return 0;
}

Output

 3.500000
// Java program for
// Average of first n natural numbers
public class Average
{
	public void findAverage(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		double sum = (n * (n + 1)) / 2.0;
		// Calculate Average
		double average = sum / n;
		// Display calculated result
		System.out.print("\n " + average);
	}
	public static void main(String[] args)
	{
		Average task = new Average();
		int n = 6;
		/*
		    n = 6
		    ---------------------------
		    1 + 2 + 3 + 4 + 5 + 6 = (21)
		    ----------------------------
		    21
		    -- = 3.5
		     6 

		*/
		task.findAverage(n);
	}
}

Output

 3.5
// Include header file
#include <iostream>

using namespace std;
// C++ program for
// Average of first n natural numbers
class Average
{
	public: void findAverage(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		double sum = (n *(n + 1)) / 2.0;
		// Calculate Average
		double average = sum / n;
		// Display calculated result
		cout << "\n " << average;
	}
};
int main()
{
	Average *task = new Average();
	int n = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	task->findAverage(n);
	return 0;
}

Output

 3.5
// Include namespace system
using System;
// Csharp program for
// Average of first n natural numbers
public class Average
{
	public void findAverage(int n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		double sum = (n * (n + 1)) / 2.0;
		// Calculate Average
		double average = sum / n;
		// Display calculated result
		Console.Write("\n " + average);
	}
	public static void Main(String[] args)
	{
		Average task = new Average();
		int n = 6;
		/*
		    n = 6
		    ---------------------------
		    1 + 2 + 3 + 4 + 5 + 6 = (21)
		    ----------------------------
		    21
		    -- = 3.5
		     6 
		*/
		task.findAverage(n);
	}
}

Output

 3.5
package main
import "fmt"
// Go program for
// Average of first n natural numbers
type Average struct {}
func getAverage() * Average {
	var me *Average = &Average {}
	return me
}
func(this Average) findAverage(n int) {
	if n <= 0 {
		return
	}
	// Calculate sum of n natural number
	// Formula = (n × (n + 1)) / 2.0
	var sum float64 = float64(n * (n + 1)) / 2.0
	// Calculate Average
	var average float64 = sum / float64(n)
	// Display calculated result
	fmt.Print("\n ", average)
}
func main() {
	var task * Average = getAverage()
	var n int = 6
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	task.findAverage(n)
}

Output

 3.5
<?php
// Php program for
// Average of first n natural numbers
class Average
{
	public	function findAverage($n)
	{
		if ($n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		$sum = ($n * ($n + 1)) / 2.0;
		// Calculate Average
		$average = $sum / $n;
		// Display calculated result
		echo("\n ".$average);
	}
}

function main()
{
	$task = new Average();
	$n = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	$task->findAverage($n);
}
main();

Output

 3.5
// Node JS program for
// Average of first n natural numbers
class Average
{
	findAverage(n)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		var sum = (n * (n + 1)) / 2.0;
		// Calculate Average
		var average = sum / n;
		// Display calculated result
		process.stdout.write("\n " + average);
	}
}

function main()
{
	var task = new Average();
	var n = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	task.findAverage(n);
}
main();

Output

 3.5
#  Python 3 program for
#  Average of first n natural numbers
class Average :
	def findAverage(self, n) :
		if (n <= 0) :
			return
		
		#  Calculate sum of n natural number
		#  Formula = (n × (n + 1)) / 2.0
		sum = (n * (n + 1)) / 2.0
		#  Calculate Average
		average = sum / n
		#  Display calculated result
		print("\n ", average, end = "")
	

def main() :
	task = Average()
	n = 6
	#    n = 6
	#    ---------------------------
	#    1 + 2 + 3 + 4 + 5 + 6 = (21)
	#    ----------------------------
	#    21
	#    -- = 3.5
	#     6 
	task.findAverage(n)

if __name__ == "__main__": main()

Output

  3.5
#  Ruby program for
#  Average of first n natural numbers
class Average 
	def findAverage(n) 
		if (n <= 0) 
			return
		end

		#  Calculate sum of n natural number
		#  Formula = (n × (n + 1)) / 2.0
		sum = (n * (n + 1)) / 2.0
		#  Calculate Average
		average = sum / n
		#  Display calculated result
		print("\n ", average)
	end

end

def main() 
	task = Average.new()
	n = 6
	#    n = 6
	#    ---------------------------
	#    1 + 2 + 3 + 4 + 5 + 6 = (21)
	#    ----------------------------
	#    21
	#    -- = 3.5
	#     6 
	task.findAverage(n)
end

main()

Output

 3.5
// Scala program for
// Average of first n natural numbers
class Average()
{
	def findAverage(n: Int): Unit = {
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		var sum: Double = (n * (n + 1)) / 2.0;
		// Calculate Average
		var average: Double = sum / n;
		// Display calculated result
		print("\n " + average);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Average = new Average();
		var n: Int = 6;
		/*
		    n = 6
		    ---------------------------
		    1 + 2 + 3 + 4 + 5 + 6 = (21)
		    ----------------------------
		    21
		    -- = 3.5
		     6 
		*/
		task.findAverage(n);
	}
}

Output

 3.5
// Swift 4 program for
// Average of first n natural numbers
class Average
{
	func findAverage(_ n: Int)
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		let sum: Double = Double(n * (n + 1)) / 2.0;
		// Calculate Average
		let average: Double = sum / Double(n);
		// Display calculated result
		print("\n ", average, terminator: "");
	}
}
func main()
{
	let task: Average = Average();
	let n: Int = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	task.findAverage(n);
}
main();

Output

  3.5
// Kotlin program for
// Average of first n natural numbers
class Average
{
	fun findAverage(n: Int): Unit
	{
		if (n <= 0)
		{
			return;
		}
		// Calculate sum of n natural number
		// Formula = (n × (n + 1)) / 2.0
		val sum: Double = (n * (n + 1)) / 2.0;
		// Calculate Average
		val average: Double = sum / n;
		// Display calculated result
		print("\n " + average);
	}
}
fun main(args: Array < String > ): Unit
{
	val task: Average = Average();
	val n: Int = 6;
	/*
	    n = 6
	    ---------------------------
	    1 + 2 + 3 + 4 + 5 + 6 = (21)
	    ----------------------------
	    21
	    -- = 3.5
	     6 
	*/
	task.findAverage(n);
}

Output

 3.5

Time Complexity

The time complexity of this algorithm is constant (O(1)) because the calculations involve basic arithmetic operations that do not depend on the input size.

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