# Average of first n odd naturals numbers

• Last Updated : 22 Jun, 2022

Given a Number n then find the Average of first n odd numbers
1 + 3 + 5 + 7 + 9 +………….+ (2n – 1)
Examples :

```Input  : 5
Output : 5
(1 + 3 + 5 + 7 + 9)/5 = 5

Input  : 10
Output : 10
(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)/10 =10```

Method 1 ( Naive Approach:)
A simple solution is to iterate loop form 1 to n time. Through sum of all odd numbers and divided by n.This solution take O(N) time.

## C++

 `// A  C++ program to find average of``// sum of first n odd natural numbers.``#include ``using` `namespace` `std;` `// Returns the Avg of``// first n odd numbers``int` `avg_of_odd_num(``int` `n)``{` `    ``// sum of first n odd number``    ``int` `sum = 0;``    ``for` `(``int` `i = 0; i < n; i++)``        ``sum += (2 * i + 1);` `    ``// Average of first``    ``// n odd numbers``    ``return` `sum / n;``}` `// Driver Code``int` `main()``{``    ``int` `n = 20;``    ``cout << avg_of_odd_num(n);``    ``return` `0;``}`

## Java

 `// Java program to find average of``// sum of first n odd natural numbers.``import` `java.io.*;` `class` `GFG {` `    ``// Returns the Avg of``    ``// first n odd numbers``    ``static` `int` `avg_of_odd_num(``int` `n)``    ``{` `        ``// sum of first n odd number``        ``int` `sum = ``0``;` `        ``for` `(``int` `i = ``0``; i < n; i++)``            ``sum += (``2` `* i + ``1``);` `        ``// Average of first``        ``// n odd numbers``        ``return` `sum / n;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``int` `n = ``20``;``        ``avg_of_odd_num(n);` `        ``System.out.println(avg_of_odd_num(n));``    ``}``}` `// This code is contributed by vt_m`

## Python3

 `# A Python 3 program``# to find average of``# sum of first n odd``# natural numbers.` `# Returns the Avg of``# first n odd numbers``def` `avg_of_odd_num(n) :` `    ``# sum of first n odd number``    ``sm ``=` `0``    ``for` `i ``in` `range``(``0``, n) :``        ``sm ``=` `sm ``+` `(``2` `*` `i ``+` `1``)``     ` `    ``# Average of first``    ``# n odd numbers``    ``return` `sm``/``/``n` ` ` `# Driver Code``n ``=` `20``print``(avg_of_odd_num(n))`  `# This code is contributed``# by Nikita Tiwari.`

## C#

 `// C# program to find average``// of sum of first n odd``// natural numbers.``using` `System;` `class` `GFG {` `    ``// Returns the Avg of``    ``// first n odd numbers``    ``static` `int` `avg_of_odd_num(``int` `n)``    ``{` `        ``// sum of first n odd number``        ``int` `sum = 0;` `        ``for` `(``int` `i = 0; i < n; i++)``            ``sum += (2 * i + 1);` `        ``// Average of first``        ``// n odd numbers``        ``return` `sum / n;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{` `        ``int` `n = 20;``        ``avg_of_odd_num(n);` `        ``Console.Write(avg_of_odd_num(n));``    ``}``}` `// This code is contributed by``// Smitha Dinesh Semwal`

## PHP

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## Javascript

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Output :

` 20`

Time Complexity: O(n)

Auxiliary Space: O(1)
Method 2 (Efficient Approach:)
The idea is the sum of first n odd number is n2, for find the Average of first n odd numbers so it is divide by n, hence formula is n2/n = n. it take O(1) time.

`                           Avg of sum of first N odd Numbers = N`

## C++

 `// CPP Program to find the average``// of sum of first n odd numbers``#include ``using` `namespace` `std;` `// Return the average of sum``// of first n odd numbers``int` `avg_of_odd_num(``int` `n)``{``    ``return` `n;``}` `// Driver Code``int` `main()``{``    ``int` `n = 8;``    ``cout << avg_of_odd_num(n);``    ``return` `0;``}`

## Java

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

## Python3

 `# Python 3 Program to``# find the average``# of sum of first n``# odd numbers` `# Return the average of sum``# of first n odd numbers``def` `avg_of_odd_num(n) :``    ``return` `n``    `  `# Driver Code``n ``=` `8``print``(avg_of_odd_num(n))`  `# This code is contributed``# by Nikita Tiwari.`

## C#

 `// C# Program to find the average``// of sum of first n odd numbers``using` `System;` `class` `GFG {``    ``// Return the average of sum``    ``// of first n odd numbers``    ``static` `int` `avg_of_odd_num(``int` `n)``    ``{``        ``return` `n;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``int` `n = 8;``        ``Console.Write(avg_of_odd_num(n));``    ``}``}``// This code is contributed by``// Smitha Dinesh Semwal`

## PHP

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## Javascript

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Output :

` 8`

Time Complexity : O(1)

Space Complexity: O(1) since using constant variables

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 = 1, d = 2, applying these values to e. q.,
(i), we get
Sum = (n/2) * [2*1 + (n-1)*2]
= (n/2) * [2 + 2*n - 2]
= (n/2) * (2*n)
= n*n
= n2

Avg of first n odd numbers = n2/n
= n```

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