Sum of first n even numbers

Given a number n. The problem is to find the sum of first n even numbers.


Examples:

Input : n = 4
Output : 20
Sum of first 4 even numbers
= (2 + 4 + 6 + 8) = 20 

Input : n = 20
Output : 420



Naive Approach: Iterate through the first n even numbers and add them.

C++

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// C++ implementation to find sum of
// first n even numbers
#include <bits/stdc++.h>
  
using namespace std;
  
// function to find sum of
// first n even numbers
int evenSum(int n)
{
    int curr = 2, sum = 0;
  
    // sum of first n even numbers
    for (int i = 1; i <= n; i++) {
        sum += curr;
  
        // next even number
        curr += 2;
    }
  
    // required sum
    return sum;
}
  
// Driver program to test above
int main()
{
    int n = 20;
    cout << "Sum of first " << n
         << " Even numbers is: " << evenSum(n);
    return 0;
}

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Java

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// Java implementation to find sum 
// of first n even numbers
import java.util.*;
import java.lang.*;
  
public class GfG{
      
    // function to find sum of
    // first n even numbers
    static int evenSum(int n)
    {
        int curr = 2, sum = 0;
  
        // sum of first n even numbers
        for (int i = 1; i <= n; i++) {
            sum += curr;
  
            // next even number
            curr += 2;
        }
  
        // required sum
        return sum;     
    }
      
    // driver function
    public static void main(String argc[])
    {
        int n = 20;
        System.out.println("Sum of first " + n +
                          " Even numbers is: "
                          evenSum(n));
    }
  
}
  
// This code is contributed by Prerna Saini

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Python3

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# Python3 implementation to find sum of
# first n even numbers
      
# function to find sum of
# first n even numbers
def evensum(n):
    curr = 2
    sum = 0
    i = 1
      
    # sum of first n even numbers
    while i <= n:
        sum += curr
          
        # next even number
        curr += 2
        i = i + 1
    return sum
  
# Driver Code
n = 20
print("sum of first ", n, "even number is: ",
      evensum(n))
  
# This article is contributed by rishabh_jain

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C#

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// C# implementation to find sum
// of first n even numbers
using System;
  
public class GfG {
  
    // function to find sum of
    // first n even numbers
    static int evenSum(int n)
    {
        int curr = 2, sum = 0;
  
        // sum of first n even numbers
        for (int i = 1; i <= n; i++) {
            sum += curr;
  
            // next even number
            curr += 2;
        }
  
        // required sum
        return sum;
    }
  
    // driver function
    public static void Main()
    {
        int n = 20;
          
        Console.WriteLine("Sum of first " + n 
         + " Even numbers is: " + evenSum(n));
    }
}
  
// This code is contributed by vt-m.

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Output:

Sum of first 20 Even numbers is: 420

Time Complexity: O(n).

Efficient Approach: By applying the formula given below.

                 Sum of first n even numbers = n * (n + 1).

Proof:

Sum of first n terms of an A.P.(Arithmetic Progression)
= (n/2) * [2*a + (n-1)*d].....(i)
where, a is the first term of the series and d is
the difference between the adjacent terms of the series.

Here, a = 2, d = 2, applying these values to eq.(i), we get
Sum = (n/2) * [2*2 + (n-1)*2]
    = (n/2) * [4 + 2*n - 2]
    = (n/2) * (2*n + 2)
    = n * (n + 1)

C++

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// C++ implementation to find sum of
// first n even numbers
#include <bits/stdc++.h>
using namespace std;
  
// function to find sum of
// first n even numbers
int evenSum(int n)
{
    // required sum
    return (n * (n + 1));
}
  
// Driver program to test above
int main()
{
    int n = 20;
    cout << "Sum of first " << n
         << " Even numbers is: " << evenSum(n);
    return 0;
}

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Java

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// Java implementation to find sum
// of first n even numbers
import java.util.*;
import java.lang.*;
  
public class GfG{
      
    // function to find sum of
    // first n even numbers
    static int evenSum(int n)
    {
        // required sum
        return (n * (n + 1));
    }
      
    // driver function
    public static void main(String argc[])
    {
        int n = 20;
        System.out.println("Sum of first " + n +
                          " Even numbers is: " +
                            evenSum(n));
    }
}
  
  
// This code is contributed by Prerna Saini

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Python3

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# Python3 implementation to find 
# sum of first n even numbers
      
# function to find sum of
# first n even numbers
def evensum(n):
    return n * (n + 1)
  
# Driver Code
n = 20
print("sum of first", n, "even number is: ",
       evensum(n))
  
# This article is contributed by rishabh_jain

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C#

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// C# implementation to find sum
// of first n even numbers'
using System;
  
public class GfG {
  
    // function to find sum of
    // first n even numbers
    static int evenSum(int n)
    {
          
        // required sum
        return (n * (n + 1));
    }
  
    // driver function
    public static void Main()
    {
        int n = 20;
          
        Console.WriteLine("Sum of first " + n 
        + " Even numbers is: " + evenSum(n));
    }
}
  
// This code is contributed by vt_m

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PHP

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<?php
// PHP implementation 
// to find sum of 
// first n even numbers
  
// function to find sum of
// first n even numbers
function evenSum($n)
{
    // required sum
    return ($n * ($n + 1));
}
  
// Driver Code
$n = 20;
echo "Sum of first " , $n,
    " Even numbers is: "
              evenSum($n);
  
// This code is contributed 
// by akt_mit
?>

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Output:

Sum of first 20 Even numbers is: 420

Time Complexity: O(1).



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