# Series summation if T(n) is given and n is very large

Given a sequence whose nth term is

T(n) = n2 – (n – 1)2

The task is to evaluate the sum of first n terms i.e.

S(n) = T(1) + T(2) + T(3) + … + T(n)

Print S(n) mod (109 + 7).

Examples:

Input: n = 3
Output: 9
S(3) = T(1) + T(2) + T(3) = (12 – 02) + (22 – 12) + (32 – 22) = 1 + 3 + 5 = 9

Input: n = 10
Output: 100

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: If we try to find out some initial terms of the sequence by putting n = 1, 2, 3, … in T(n) = n2 – (n – 1)2, we find the sequence 1, 3, 5, …
Hence, we find an A.P. where first term is 1 and d (common difference between consecutive
terms) is 2.
The formula for the sum of n terms of A.P is

S(n) = n / 2 [ 2 * a + (n – 1) * d ]

where a is the first term.
So, putting a = 1 and d = 2, we get

S(n) = n2

.

Below is the implementation of above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define ll long long int ` `#define MOD 1000000007 ` ` `  `// Function to return the sum ` `// of the given series ` `int` `sumOfSeries(``int` `n) ` `{ ` `    ``ll ans = (ll)``pow``(n % MOD, 2); ` ` `  `    ``return` `(ans % MOD); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``cout << sumOfSeries(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` `     `  `public` `static` `final` `int` `MOD = ``1000000007``; ` ` `  `// Function to return the sum ` `// of the given series ` `static` `int` `sumOfSeries(``int` `n) ` `{ ` `    ``int` `ans = (``int``)Math.pow(n % MOD, ``2``); ` ` `  `    ``return` `(ans % MOD); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``10``; ` `    ``System.out.println(sumOfSeries(n)); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech. `

## Python3

 `# Python 3 implementation of the approach ` `from` `math ``import` `pow` ` `  `MOD ``=` `1000000007` ` `  `# Function to return the sum ` `# of the given series ` `def` `sumOfSeries(n): ` `    ``ans ``=` `pow``(n ``%` `MOD, ``2``) ` ` `  `    ``return` `(ans ``%` `MOD) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `10` `    ``print``(``int``(sumOfSeries(n))) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `const` `int` `MOD = 1000000007; ` ` `  `// Function to return the sum ` `// of the given series ` `static` `int` `sumOfSeries(``int` `n) ` `{ ` `    ``int` `ans = (``int``)Math.Pow(n % MOD, 2); ` ` `  `    ``return` `(ans % MOD); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 10; ` `    ``Console.Write(sumOfSeries(n)); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Akanksha Rai `

## PHP

 ` `

Output:

```100
``` 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.

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.