# 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)

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : jit_t

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.