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Sum of initial N Even natural numbers

The problem revolves around finding the sum of the first n even natural numbers. Even natural numbers are those positive integers that are divisible by 2. The task is to calculate the sum of the initial n even natural numbers efficiently.

Problem Statement

Given a positive integer n, the objective is to calculate the sum of the first n even natural numbers.

Example

Consider n = 5 as an example. Even natural numbers are: 2, 4, 6, 8, 10. The sum of these numbers is 2 + 4 + 6 + 8 + 10 = 30.

Idea to Solve

The problem can be addressed by employing the mathematical properties of arithmetic progression. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. The sum of an arithmetic progression can be calculated using the formula: sum = n * (first term + last term) / 2.

In this case, the first term is 2 (the smallest even natural number) and the last term is 2n (the nth even natural number). Thus, the sum formula becomes: sum = n * (2 + 2n) / 2 = n * (n + 1).

Pseudocode

function sumOfEven(n)
    result = n * (n + 1)
    print "Sum of", n, "Even natural numbers is:", result

Algorithm Explanation

  1. Calculate the sum of the first n even natural numbers using the formula n * (n + 1).
  2. Print the result.

Code Solution

/*
    C program for
    Sum of initial N Even natural numbers
*/
#include <stdio.h>

void sumOfEven(int n)
{
	int result = n *(n + 1);
	// Display calculated result
	printf(" Sum of %d Even natural numbers is  : %d \n", n, result);
}
int main(int argc, char const *argv[])
{
	/*
	   Test A

	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	sumOfEven(10);
	/*
	   Test B

	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	sumOfEven(7);
	return 0;
}

Output

 Sum of 10 Even natural numbers is  : 110
 Sum of 7 Even natural numbers is  : 56
/*
    Java program for
    Sum of initial N Even natural numbers
*/
public class NaturalNumbers
{
	public void sumOfEven(int n)
	{
		int result = n * (n + 1);
		// Display calculated result
		System.out.print("\n Sum of " + 
                         n + " Even natural numbers is : " + 
                         result);
	}
	public static void main(String[] args)
	{
		NaturalNumbers task = new NaturalNumbers();
		/*
		   Test A

		   n = 10
		  
		   (2) + (4) + (6) + (8) + (10) + 
		   (12) + (14) + (16) + (18) + (20)
		   ----------------------------------------
		   Result = 110
		   
		*/
		task.sumOfEven(10);
		/*
		   Test B

		   n = 7
		   
		   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
		   ----------------------------------------
		   Result = 56
		*/
		task.sumOfEven(7);
	}
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
// Include header file
#include <iostream>

using namespace std;
/*
    C++ program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers
{
	public: void sumOfEven(int n)
	{
		int result = n *(n + 1);
		// Display calculated result
		cout << "\n Sum of " << n 
      		 << " Even natural numbers is : " 
             << result;
	}
};
int main()
{
	NaturalNumbers *task = new NaturalNumbers();
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	task->sumOfEven(10);
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	task->sumOfEven(7);
	return 0;
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
// Include namespace system
using System;
/*
    Csharp program for
    Sum of initial N Even natural numbers
*/
public class NaturalNumbers
{
	public void sumOfEven(int n)
	{
		int result = n * (n + 1);
		// Display calculated result
		Console.Write("\n Sum of " + 
                      n + " Even natural numbers is : " + 
                      result);
	}
	public static void Main(String[] args)
	{
		NaturalNumbers task = new NaturalNumbers();
		/*
		   Test A
		   n = 10
		  
		   (2) + (4) + (6) + (8) + (10) + 
		   (12) + (14) + (16) + (18) + (20)
		   ----------------------------------------
		   Result = 110
		   
		*/
		task.sumOfEven(10);
		/*
		   Test B
		   n = 7
		   
		   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
		   ----------------------------------------
		   Result = 56
		*/
		task.sumOfEven(7);
	}
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
package main
import "fmt"
/*
    Go program for
    Sum of initial N Even natural numbers
*/

func sumOfEven(n int) {
	var result int = n * (n + 1)
	// Display calculated result
	fmt.Print("\n Sum of ", n, " Even natural numbers is : ", result)
}
func main() {
	
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	sumOfEven(10)
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	sumOfEven(7)
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
<?php
/*
    Php program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers
{
	public	function sumOfEven($n)
	{
		$result = $n * ($n + 1);
		// Display calculated result
		echo("\n Sum of ".$n.
			" Even natural numbers is : ".$result);
	}
}

function main()
{
	$task = new NaturalNumbers();
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	$task->sumOfEven(10);
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	$task->sumOfEven(7);
}
main();

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
/*
    Node JS program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers
{
	sumOfEven(n)
	{
		var result = n * (n + 1);
		// Display calculated result
		process.stdout.write("\n Sum of " + 
                             n + " Even natural numbers is : " + 
                             result);
	}
}

function main()
{
	var task = new NaturalNumbers();
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	task.sumOfEven(10);
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	task.sumOfEven(7);
}
main();

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
#    Python 3 program for
#    Sum of initial N Even natural numbers
class NaturalNumbers :
	def sumOfEven(self, n) :
		result = n * (n + 1)
		#  Display calculated result
		print("\n Sum of", n ,
              "Even natural numbers is :", 
              result, end = "")
	

def main() :
	task = NaturalNumbers()
	#   Test A
	#   n = 10
	#   (2) + (4) + (6) + (8) + (10) + 
	#   (12) + (14) + (16) + (18) + (20)
	#   ----------------------------------------
	#   Result = 110
	task.sumOfEven(10)
	#   Test B
	#   n = 7
	#   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	#   ----------------------------------------
	#   Result = 56
	task.sumOfEven(7)

if __name__ == "__main__": main()

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
#    Ruby program for
#    Sum of initial N Even natural numbers
class NaturalNumbers 
	def sumOfEven(n) 
		result = n * (n + 1)
		#  Display calculated result
		print("\n Sum of ", 
              n ," Even natural numbers is : ", 
              result)
	end

end

def main() 
	task = NaturalNumbers.new()
	#   Test A
	#   n = 10
	#   (2) + (4) + (6) + (8) + (10) + 
	#   (12) + (14) + (16) + (18) + (20)
	#   ----------------------------------------
	#   Result = 110
	task.sumOfEven(10)
	#   Test B
	#   n = 7
	#   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	#   ----------------------------------------
	#   Result = 56
	task.sumOfEven(7)
end

main()

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
/*
    Scala program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers()
{
	def sumOfEven(n: Int): Unit = {
		var result: Int = n * (n + 1);
		// Display calculated result
		print("\n Sum of " + 
              n + " Even natural numbers is : " + result);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: NaturalNumbers = new NaturalNumbers();
		/*
		   Test A
		   n = 10
		  
		   (2) + (4) + (6) + (8) + (10) + 
		   (12) + (14) + (16) + (18) + (20)
		   ----------------------------------------
		   Result = 110
		   
		*/
		task.sumOfEven(10);
		/*
		   Test B
		   n = 7
		   
		   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
		   ----------------------------------------
		   Result = 56
		*/
		task.sumOfEven(7);
	}
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
/*
    Swift 4 program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers
{
	func sumOfEven(_ n: Int)
	{
		let result: Int = n * (n + 1);
		// Display calculated result
		print("\n Sum of", n ,
              "Even natural numbers is :", 
              result, terminator: "");
	}
}
func main()
{
	let task: NaturalNumbers = NaturalNumbers();
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	task.sumOfEven(10);
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	task.sumOfEven(7);
}
main();

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56
/*
    Kotlin program for
    Sum of initial N Even natural numbers
*/
class NaturalNumbers
{
	fun sumOfEven(n: Int): Unit
	{
		val result: Int = n * (n + 1);
		// Display calculated result
		print("\n Sum of " + n + 
              " Even natural numbers is : " + result);
	}
}
fun main(args: Array < String > ): Unit
{
	val task: NaturalNumbers = NaturalNumbers();
	/*
	   Test A
	   n = 10
	  
	   (2) + (4) + (6) + (8) + (10) + 
	   (12) + (14) + (16) + (18) + (20)
	   ----------------------------------------
	   Result = 110
	   
	*/
	task.sumOfEven(10);
	/*
	   Test B
	   n = 7
	   
	   (2) + (4) + (6) + (8) + (10) + (12) + (14) 
	   ----------------------------------------
	   Result = 56
	*/
	task.sumOfEven(7);
}

Output

 Sum of 10 Even natural numbers is : 110
 Sum of 7 Even natural numbers is : 56

Time Complexity

The time complexity of this algorithm is constant, O(1), since it involves only a few mathematical operations that do not depend on the input size. The space complexity is also constant, as it uses a fixed number of variables.

Last updated on by Kalkicode




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