# Average of first n even natural numbers

Given a number n then Find the Average of first n even natural numbers

Ex.= 2 + 4 + 6 + 8 + 10 + 12 +………+ 2n. **Examples :**

Input : 7 Output : 8 (2 + 4 + 6 + 8 + 10 + 12 + 14)/7 = 8 Input : 5 Output : 6 (2 + 4 + 6 + 8 + 10)/5 = 6

**Naive Approach:-** In this program iterate the loop , finding total sum of first n even numbers and divided by n.it take 0(N) time.

## C++

`// C++ implementation to find Average` `// of sum of first n natural even numbers` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function to find average of` `// sum of first n even numbers` `int` `avg_of_even_num(` `int` `n)` `{` ` ` `// sum of first n even numbers` ` ` `int` `sum = 0;` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `sum += 2*i;` ` ` `// calculating Average` ` ` `return` `sum/n;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 9;` ` ` `cout << avg_of_even_num(n);` ` ` `return` `0;` `}` |

## Java

`// java implementation to find Average` `// of sum of first n natural even number` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `// function to find average of` ` ` `// sum of first n even numbers` ` ` `static` `int` `avg_of_even_num(` `int` `n)` ` ` `{` ` ` ` ` `// sum of first n even numbers` ` ` `int` `sum = ` `0` `;` ` ` ` ` ` ` `for` `(` `int` `i = ` `1` `; i <= n; i++)` ` ` `sum += ` `2` `*i;` ` ` `// calculating Average` ` ` `return` `(sum / n);` ` ` `}` ` ` `public` `static` `void` `main (String[] args) {` ` ` ` ` `int` `n = ` `9` `;` ` ` `System.out.print(avg_of_even_num(n));` ` ` ` ` `}` `}` `// this code is contributed by 'vt_m'` |

## Python3

`# Python3 implementation to` `# find Average of sum of` `# first n natural even` `# number` `# Function to find average` `# of sum of first n even` `# numbers` `def` `avg_of_even_num(n):` ` ` ` ` `# sum of first n even` ` ` `# numbers` ` ` `sum` `=` `0` ` ` `for` `i ` `in` `range` `(` `1` `, n ` `+` `1` `):` ` ` `sum` `=` `sum` `+` `2` `*` `i` ` ` ` ` `# calculating Average` ` ` `return` `sum` `/` `n` `n` `=` `9` `print` `(avg_of_even_num(n))` `# This code is contributed by upendra singh bartwal` |

## C#

`// C# implementation to find` `// Average of sum of first` `// n natural even number` `using` `System;` `class` `GFG {` ` ` ` ` `// function to find average of` ` ` `// sum of first n even numbers` ` ` `static` `int` `avg_of_even_num(` `int` `n)` ` ` `{` ` ` ` ` `// sum of first n even numbers` ` ` `int` `sum = 0;` ` ` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `sum += 2 * i;` ` ` `// calculating Average` ` ` `return` `(sum / n);` ` ` `}` ` ` ` ` `// driver code` ` ` `public` `static` `void` `Main () {` ` ` ` ` `int` `n = 9;` ` ` `Console.Write(avg_of_even_num(n));` ` ` ` ` `}` `}` `// This code is contributed by 'vt_m'` |

## PHP

`<?php` `// PHP implementation to find Average` `// of sum of first n natural even numbers` `// function to find average of` `// sum of first n even numbers` `function` `avg_of_even_num(` `$n` `)` `{` ` ` `// sum of first n even numbers` ` ` `$sum` `= 0;` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$sum` `+= 2 * ` `$i` `;` ` ` `// calculating Average` ` ` `return` `$sum` `/ ` `$n` `;` `}` `// Driver Code` `$n` `= 9;` `echo` `(avg_of_even_num(` `$n` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// javascript implementation to find Average` `// of sum of first n natural even numbers` `// function to find average of` `// sum of first n even numbers` `function` `avg_of_even_num( n)` `{` ` ` `// sum of first n even numbers` ` ` `let sum = 0;` ` ` `for` `(let i = 1; i <= n; i++)` ` ` `sum += 2*i;` ` ` `// calculating Average` ` ` `return` `sum/n;` `}` `// Driver Code` ` ` `let n = 9;` ` ` `document.write(avg_of_even_num(n));` `// This code is contributed by todaysgaurav` `</script>` |

**Output :**

10

**Time Complexity : O(N) ****Method 2 :- **The idea is the sum of first n even number is n(n+1), for find the Average of first n even numbers divide by n, hence formula is **n(n + 1) / n = ( n + 1)**. i.e. Average of first n even numbers is **n+1**. it take 0(1) time.

Avg of sum of N even natural number = (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), get Sum = (n/2) * [2*2 + (n-1)*2] = (n/2) * [4 + 2*n - 2] = (n/2) * (2*n + 2) = n * (n + 1) finding the Avg so divided by n = n*(n+1)/n = (n+1)

## C++

`// CPP Program to find the average` `// of sum of first n even numbers` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Return the average of sum` `// of first n even numbers` `int` `avg_of_even_num(` `int` `n)` `{` ` ` `return` `n+1;` `}` ` ` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 8;` ` ` `cout << avg_of_even_num(n) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java Program to find the average` `// of sum of first n even numbers` `import` `java.io.*;` `class` `GFG` `{` ` ` `// Return the average of sum` ` ` `// of first n even numbers` ` ` `static` `int` `avg_of_even_num(` `int` `n)` ` ` `{` ` ` `return` `n + ` `1` `;` ` ` `}` ` ` ` ` `public` `static` `void` `main (String[] args) {` ` ` ` ` `int` `n = ` `8` `;` ` ` `System.out.println(avg_of_even_num(n));` ` ` ` ` `}` `}` `// This code is contributed by vt_m` |

## Python3

`# Python 3 Program to` `# find the average` `# of sum of first n` `# even numbers` `# Return the average of sum` `# of first n even numbers` `def` `avg_of_even_num(n) :` ` ` ` ` `return` `n` `+` `1` ` ` ` ` `# Driven Program` `n ` `=` `8` `print` `(avg_of_even_num(n))` `# This code is contributed` `# by Nikita Tiwari.` |

## C#

`// C# Program to find the average` `// of sum of first n even numbers` `using` `System;` `class` `GFG {` ` ` `// Return the average of sum` ` ` `// of first n even numbers` ` ` `static` `int` `avg_of_even_num(` `int` `n)` ` ` `{` ` ` `return` `n + 1;` ` ` `}` ` ` ` ` `// driver code ` ` ` `public` `static` `void` `Main () {` ` ` ` ` `int` `n = 8;` ` ` `Console.Write(avg_of_even_num(n));` ` ` ` ` `}` `}` `// This code is contributed by vt_m` |

## PHP

`<?php` `// PHP Program to find the average` `// of sum of first n even numbers` `// Return the average of sum` `// of first n even numbers` `function` `avg_of_even_num(` `$n` `)` `{` ` ` `return` `$n` `+ 1;` `}` ` ` `// Driver Code` `$n` `= 8;` `echo` `(avg_of_even_num(` `$n` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// javascript Program to find the average` `// of sum of first n even numbers` `// Return the average of sum` `// of first n even numbers` `function` `avg_of_even_num(n)` `{` ` ` `return` `n + 1;` `}` `var` `n = 8;` `document.write(avg_of_even_num(n));` `// This code is contributed by Amit Katiyar` `</script>` |

Output:

9

**Time Complexity : O(1) **

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