Average of even numbers till a given even number

• Last Updated : 22 Jun, 2022

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++

 `// Program to find average of even numbers``// till a given even number.``#include `` ` `// 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;``}`

Java

 `// 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.*/`

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``    ` `    ``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.`

C#

 `// 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.*/`

PHP

 `= 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.``?>`

Javascript

 ``

Output:

`9`

Time Complexity: O(n)

Auxiliary Space: O(1)
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++

 `// Program to find average of even numbers``// till a given even nend number.``#include ``using` `namespace` `std;`` ` `// Function to calculate the average``// of even numbers``int` `averageEven(``int` `n)``{``    ``if` `(n % 2 != 0) {``        ``cout<<``"Invalid Input"``;``        ``return` `-1;``    ``}`` ` `    ``return` `(n + 2) / 2;``}`` ` `// driver function``int` `main()``{``    ``int` `n = 16;``    ``cout<

C

 `// Program to find average of even numbers``// till a given even number.``#include `` ` `// 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;``}`

Java

 `// 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.*/`

Python3

 `# 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.`

C#

 `// 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.*/`

PHP

 ``

Javascript

 ``

Output :

`9`

Time complexity: O(1) since performing constant operations

Space Complexity: O(1) since using constant variables

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