Average of even numbers till a given even number

Given an even number n, find the average of even numbers from 1 to n.

Examples :

Input : 10
Output : 6
Explanation:
(2 + 4 + 6 + 8 + 10 )/5
= 30/5
= 6 
 
Input : 100
Output : 51



Method 1
We can calculate average by adding each even numbers till n and then dividing sum by count.

C++

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// Program to find average of even numbers
// till a given even number.
#include <stdio.h>
   
// Function to calculate the average
// of even numbers
int averageEven(int n)
{
    if (n % 2 != 0) {
        printf("Invalid Input");
        return -1;
    }
   
    int sum = 0, count = 0;
    while (n >= 2) {
   
        // count even numbers
        count++;
   
        // store the sum of even numbers
        sum += n;
   
        n = n - 2;
    }
    return sum / count;
}
   
// driver function
int main()
{
    int n = 16;
    printf("%d", averageEven(n));
    return 0;
}

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Java

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// Program to find average of even numbers
// till a given even number.
import java.io.*;
   
class GFG {
   
    // Function to calculate the average
    // of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        System.out.println("Invalid Input");
            return -1;
        }
   
        int sum = 0, count = 0;
        while (n >= 2) {
   
         // count even numbers
         count++;
   
         // store the sum of even numbers
         sum += n;
   
         n = n - 2;
        }
        return sum / count;
    }
   
    // driver function
    public static void main(String args[])
    {
        int n = 16;
        System.out.println(averageEven(n));
    }
}
   
/*This code is contributed by Nikita Tiwari.*/

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Python3

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# Program to find average of
# even numbers till a given 
# even number.
  
# Function to calculate the
# average of even numbers
def averageEven(n) :
  
    if (n % 2 != 0) :
        print("Invalid Input")
        return -1
      
    sm = 0
    count = 0
  
    while (n >= 2) :
  
        # count even numbers
        count = count + 1
  
        # store the sum of even
        # numbers
        sm = sm + n
  
        n = n - 2
      
    return sm // count
  
# driver function
n = 16
print(averageEven(n))
  
# This code is contributed by Nikita Tiwari.

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C#

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// C# Program to find average 
// of even numbers till a 
// given even number.
using System;
  
class GFG {
  
    // Function to calculate the
    // average of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        Console.Write("Invalid Input");
            return -1;
        }
  
        int sum = 0, count = 0;
        while (n >= 2) {
  
        // count even numbers
        count++;
  
        // store the sum of even numbers
        sum += n;
  
        n = n - 2;
        }
        return sum / count;
    }
  
    // driver function
    public static void Main()
    {
        int n = 16;
        Console.Write(averageEven(n));
    }
}
  
/*This code is contributed by vt_m.*/

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PHP

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<?php
// PHP Program to find average of even 
// numbers till a given even number.
  
// Function to calculate the 
// average of even numbers
function averageEven( $n)
{
    if ($n % 2 != 0) 
    {
        echo("Invalid Input");
        return -1;
    }
  
    $sum = 0; 
    $count = 0;
    while ($n >= 2) 
    {
  
        // count even numbers
        $count++;
  
        // store the sum of 
        // even numbers
        $sum += $n;
  
        $n = $n - 2;
    }
    return $sum / $count;
}
  
    // Driver Code
    $n = 16;
    echo(averageEven($n));
      
//This code is contributed by vt_m.
?>

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Output:

9

Method 2
The average of even numbers can be find out only in single steps
by using the following formula :-
[n + 2 ] / 2 where n is last even number.

How does this formula work?
We know there are (n)/2 even numbers till n. For example there are two even number till 4 and there are three even numbers till 6.

Sum of first k even numbers is k * (k + 1)

Putting k = n/2, we get sum of first n/2 even numbers as n/2(n/2 + 1)

Average of first n/2 even numbers (or even numbers till n) = (n + 2)/2

C

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// Program to find average of even numbers
// till a given even number.
#include <stdio.h>
   
// Function to calculate the average
// of even numbers
int averageEven(int n)
{
    if (n % 2 != 0) {
        printf("Invalid Input");
        return -1;
    }
   
    return (n + 2) / 2;
}
   
// driver function
int main()
{
    int n = 16;
    printf("%d", averageEven(n));
    return 0;
}

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Java

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// Program to find average of even numbers
// till a given even number.
import java.io.*;
  
class GFG {
      
    // Function to calculate the average
    // of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        System.out.println("Invalid Input");
            return -1;
        }
  
        return (n + 2) / 2;
    }
  
    // driver function
    public static void main(String args[])
    {
        int n = 16;
        System.out.println(averageEven(n));
    }
}
  
/*This code is contributed by Nikita Tiwari.*/

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Python3

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# Python3 program to find average of even 
# numbers till a given even number.
  
# Function to calculate the 
# average of even numbers
def averageEven(n) :
    if (n % 2 != 0) :
        print("Invalid Input")
        return -1
      
    return (n + 2) // 2
      
# Driver function
n = 16
print(averageEven(n))
  
# This code is contributed by Nikita Tiwari.

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C#

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// C# Program to find average 
// of even numbers till a
// given even number.
using System;
  
class GFG {
      
    // Function to calculate the
    // average of even numbers
    static int averageEven(int n)
    {
        if (n % 2 != 0) {
        Console.Write("Invalid Input");
            return -1;
        }
  
        return (n + 2) / 2;
    }
  
    // driver function
    public static void Main()
    {
        int n = 16;
        Console.Write(averageEven(n));
    }
}
  
/*This code is contributed by vt_m.*/

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PHP

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<?php
// PHP Program to find average of even 
// numbers till a given even number.
  
// Function to calculate the average
// of even numbers
function averageEven( $n)
{
    if ($n % 2 != 0) 
    {
        echo("Invalid Input");
        return -1;
    }
  
    return ($n + 2) / 2;
}
  
    // Driver Code
    $n = 16;
    echo (averageEven($n));
    return 0;
  
// This code is contributed by vt_m. 
?>

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Output :

9


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Improved By : vt_m



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