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# Find sum of N terms of the series 3^3 – 2^3, 5^3 – 4^3, 7^3 – 6^3, …

• Last Updated : 16 Aug, 2022

Given a positive integer N, the task is to find the sum upto Nth term of the series:

33 – 23, 53 – 43, 73 – 63, …., till N terms

Examples:

Input: N = 10
Output: 4960

Input: N = 1
Output: 19

Naive Approach

• Initialize two int variables odd and even. Odd with value 3 and even with value 2.
• Now Iterate the for loop n times each time will calculate the current term and add it to the sum.
• In each iteration  increase odd and even value with 2.
• Return the resultant sum

## C++

 `// C++ program to find sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...`   `#include ` `using` `namespace` `std;`   `// Function to return sum of` `// N term of the series`   `int` `findSum(``int` `N)` `{` `    ``// Initialize the variable` `    ``int` `Odd = 3;` `    ``int` `Even = 2;` `    ``int` `Sum = 0;`   `    ``// Run a loop for N number of times` `    ``for` `(``int` `i = 0; i < N; i++) {`   `        ``// Calculate the current term` `        ``// and add it to the sum` `        ``Sum += (``pow``(Odd, 3)` `                ``- ``pow``(Even, 3));`   `        ``// Increase the odd and` `        ``// even with value 2` `        ``Odd += 2;` `        ``Even += 2;` `    ``}` `    ``return` `Sum;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 10;` `    ``cout << findSum(N);` `}`

## Java

 `// JAVA program to find sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...` `import` `java.util.*;` `class` `GFG ` `{`   `  ``// Function to return sum of` `  ``// N term of the series` `  ``public` `static` `int` `findSum(``int` `N)` `  ``{`   `    ``// Initialize the variable` `    ``int` `Odd = ``3``;` `    ``int` `Even = ``2``;` `    ``int` `Sum = ``0``;`   `    ``// Run a loop for N number of times` `    ``for` `(``int` `i = ``0``; i < N; i++) {`   `      ``// Calculate the current term` `      ``// and add it to the sum` `      ``Sum += (Math.pow(Odd, ``3``) - Math.pow(Even, ``3``));`   `      ``// Increase the odd and` `      ``// even with value 2` `      ``Odd += ``2``;` `      ``Even += ``2``;` `    ``}` `    ``return` `Sum;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `main(String[] args)` `  ``{` `    ``int` `N = ``10``;` `    ``System.out.print(findSum(N));` `  ``}` `}`   `// This code is contributed by Taranpreet`

## Python3

 `# Python 3 program for the above approach`   `# Function to calculate the sum` `# of first N term` `def` `findSum(N):` `    ``# Initialize the variable` `    ``Odd ``=` `3` `    ``Even ``=` `2` `    ``Sum` `=` `0`   `    ``# Run a loop for N number of times` `    ``for` `i ``in` `range``(N):`   `        ``# Calculate the current term` `        ``# and add it to the sum` `        ``Sum` `+``=` `(``pow``(Odd, ``3``) ``-` `pow``(Even, ``3``))`   `        ``# Increase the odd and` `        ``# even with value 2` `        ``Odd ``+``=` `2` `        ``Even ``+``=` `2` `        `  `    ``return` `Sum`     `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``# Value of N` `    ``N ``=` `10` `    `  `    ``# Function call to calculate` `    ``# sum of the series` `    ``print``(findSum(N))`   `# This code is contributed by Abhishek Thakur.`

## C#

 `// C# program to find sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...` `using` `System;` `class` `GFG ` `{`   `  ``// Function to return sum of` `  ``// N term of the series` `  ``public` `static` `int` `findSum(``int` `N)` `  ``{`   `    ``// Initialize the variable` `    ``int` `Odd = 3;` `    ``int` `Even = 2;` `    ``int` `Sum = 0;`   `    ``// Run a loop for N number of times` `    ``for` `(``int` `i = 0; i < N; i++) {`   `      ``// Calculate the current term` `      ``// and add it to the sum` `      ``Sum += (``int``)(Math. Pow(Odd, 3) - Math.Pow(Even, 3));`   `      ``// Increase the odd and` `      ``// even with value 2` `      ``Odd += 2;` `      ``Even += 2;` `    ``}` `    ``return` `Sum;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `Main()` `  ``{` `    ``int` `N = 10;` `    ``Console.Write(findSum(N));` `  ``}` `}`   `// This code is contributed by Samim Hossain Mondal.`

## Javascript

 ``

Output

`4960`

Time Complexity: O(N)
Auxiliary Space: O(1), since no extra space has been taken.

Efficient Approach:

The sequence is formed by using the following pattern.

For any value N the generalise form of the given sequence is-

SN = 4*N3 + 9*N2 + 6*N

Below is the implementation of the above approach:

## C++

 `// C++ program to find the sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...`   `#include ` `using` `namespace` `std;`   `// Function to return sum of` `// N term of the series`   `int` `findSum(``int` `N)` `{` `    ``return` `4 * ``pow``(N, 3) + 9 * ``pow``(N, 2) + 6 * N;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 10;` `    ``cout << findSum(N);` `}`

## Java

 `// Java program to find the sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...` `import` `java.util.*;`   `class` `GFG` `{`   `  ``// Function to return sum of` `  ``// N term of the series` `  ``static` `int` `findSum(``int` `N)` `  ``{` `    ``return` `(``int``) (``4` `* Math.pow(N, ``3``) + ``9` `* Math.pow(N, ``2``) + ``6` `* N);` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `main(String[] args)` `  ``{` `    ``int` `N = ``10``;` `    ``System.out.print(findSum(N));` `  ``}` `}`   `// This code is contributed by 29AjayKumar`

## Python3

 `# Python 3 program to find the sum of N terms of the` `# series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...`   `# Function to calculate the sum` `# of first N term` `def` `findSum(N):` `    ``return` `4` `*` `pow``(N, ``3``) ``+` `9` `*` `pow``(N, ``2``) ``+` `6` `*` `N`     `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``# Value of N` `    ``N ``=` `10` `    `  `    ``# Function call to calculate` `    ``# sum of the series` `    ``print``(findSum(N))`   `# This code is contributed by Abhishek Thakur.`

## C#

 `// C# program to find the sum of N terms of the` `// series 3^3-2^3, 5^3 - 4^3, 7^3 - 6^3, ...` `using` `System;` `class` `GFG ` `{`   `  ``// Function to return sum of` `  ``// N term of the series` `  ``static` `int` `findSum(``int` `N)` `  ``{` `    ``return` `4 * (``int``)Math.Pow(N, 3)` `      ``+ 9 * (``int``)Math.Pow(N, 2) + 6 * N;` `  ``}`   `  ``// Driver Code` `  ``public` `static` `void` `Main()` `  ``{` `    ``int` `N = 10;` `    ``Console.Write(findSum(N));` `  ``}` `}`   `// This code is contributed by ukasp.`

## Javascript

 ``

Output

`4960`

Time Complexity: O(1)
Auxiliary Space: O(1)

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