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

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

 ` `

Output:

```1330
```

Time Complexity : O(n)

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

 ` `

Output:

```1330
```

Time Complexity: O(1)

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