# Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2

• Last Updated : 15 Jun, 2022

Given a series 12 + 32 + 52 + 72 + . . . + (2*n – 1)2, find sum of the series.
Examples:

```Input : n = 4
Output : 84
Explanation :
sum = 12 + 32 + 52 + 72
= 1 + 9 + 25 + 49
= 84

Input : n = 10
Output : 1330
Explanation :
sum = 12 + 32 + 52 + 72 + 92 + 112 + 132 + 152 + 172 + 192
= 1 + 9 + 24 + 49 + . . . + 361
= 1330```

## C++

 `// Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.``#include ``using` `namespace` `std;` `// Function to find sum of series.``int` `sumOfSeries(``int` `n)``{``    ``int` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum = sum + (2 * i - 1) * (2 * i - 1);``    ``return` `sum;``}` `// Driver code``int` `main()``{``    ``int` `n = 10;` `    ``cout << sumOfSeries(n);` `    ``return` `0;``}`

## Java

 `// Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.` `import` `java.io.*;` `class` `GFG {``   ` `// Function to find sum of series.`` ``static` `int` `sumOfSeries(``int` `n)``{``    ``int` `sum = ``0``;``    ``for` `(``int` `i = ``1``; i <= n; i++)``       ``sum = sum + (``2` `* i - ``1``) * (``2` `* i - ``1``);``    ``return` `sum;``}` `// Driver code``  ``public` `static` `void`  `main(String[] args)``{``    ``int` `n = ``10``;``    ``System.out.println( sumOfSeries(n));   ``}``    ` `}`

## Python3

 `# Python Program to find sum of series``# 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.` `import` `math` `# Function to find sum of series.``def` `sumOfSeries(n):` `    ``sum` `=` `0``    ``for` `i ``in` `range``(``1``,n``+``1``):``        ``sum` `=` `sum` `+` `(``2` `*` `i ``-` `1``) ``*` `(``2` `*` `i ``-` `1``)``    ``return` `sum``    ` `# driver code``n``=` `10``print``(sumOfSeries(n))` `# This code is contributed by Gitanjali.`

## C#

 `// C# Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.``using` `System;` `class` `GFG {``    ` `// Function to find sum of series.``static` `int` `sumOfSeries(``int` `n)``{``    ``int` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum = sum + (2 * i - 1) * (2 * i - 1);``    ` `    ``return` `sum;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `n = 10;``    ``Console.Write( sumOfSeries(n));``}``}` `/* This code is contributed by vt_m*/`

## PHP

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## Javascript

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Output:

`1330`

Time Complexity : O(n)

Auxiliary Space: O(1)

Another approach : Using formula to find sum of series :

```    12 + 32 + 52 +
72 + . . . + (2*n - 1)2
= (n * (2 * n - 1) * (2 * n + 1)) / 3.

Please refer sum of squares of even and odd numbers for proof.```

## C++

 `// Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.``#include ``using` `namespace` `std;` `// Function that find sum of series.``int` `sumOfSeries(``int` `n)``{``    ``// Formula to find sum of series.``    ``return` `(n * (2 * n - 1) * (2 * n + 1)) / 3;``}` `// Driver code``int` `main()``{``    ``int` `n = 10;``    ``cout << sumOfSeries(n);``    ``return` `0;``}`

## Java

 `// Java Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.` `import` `java.io.*;``import` `java.util.*;` `class` `GFG {``    ` `// Function to find sum of series.``static` `int` `sumOfSeries(``int` `n)``{``   ``// Formula to find sum of series.``    ``return` `(n * (``2` `* n - ``1``) * (``2` `* n + ``1``)) / ``3``;` `}` `// Driver function``   ``public` `static` `void` `main (String[] args) {``   ``int` `n=``10``;``    ``System.out.println(sumOfSeries(n));``    ` `}` `}` `// This code is contributed by Gitanjali.`

## Python3

 `# Python Program to find sum of series``# 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.` `import` `math` `# Function to find sum of series.``def` `sumOfSeries(n):` `   ``# Formula to find sum of series.``    ``return` `int``((n ``*` `(``2` `*` `n ``-` `1``) ``*` `(``2` `*` `n ``+` `1``)) ``/` `3``)`` ` `# driver code``n``=``10``print``(sumOfSeries(n))` `# This code is contributed by Gitanjali.`

## C#

 `// C# Program to find sum of series``// 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2.``using` `System;` `class` `GFG {``    ` `// Function to find sum of series.``static` `int` `sumOfSeries(``int` `n)``{``    ``// Formula to find sum of series.``    ``return` `(n * (2 * n - 1) * (2 * n + 1)) / 3;``}` `// Driver function``public` `static` `void` `Main ()``{``    ``int` `n = 10;``    ``Console.Write(sumOfSeries(n));``}``}` `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output:

`1330`

Time Complexity: O(1)

Auxiliary space: O(1) since using constant variables

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