# 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 codeint 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 coden= 10print(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 codepublic static void Main(){    int n = 10;    Console.Write( sumOfSeries(n));}} /* This code is contributed by vt_m*/



## Javascript



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 codeint 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 coden=10print(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 functionpublic static void Main (){    int n = 10;    Console.Write(sumOfSeries(n));}} // This code is contributed by vt_m.



## Javascript



Output:

1330

Time Complexity: O(1)

Auxiliary space: O(1) since using constant variables

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