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# Find the sum of first N terms of the series 2*3*5, 3*5*7, 4*7*9, …

• Last Updated : 25 Mar, 2021

Given an integer N, the task is to find the sum of first N terms of the series:

(2 * 3 * 5), (3 * 5 * 7), (4 * 7 * 9), …

Examples:

Input: N = 3
Output: 387
S3 = (2 * 3 * 5) + (3 * 5 * 7) + (4 * 7 * 9) = 30 + 105 + 252 = 387
Input: N = 5
Output: 1740

Approach: Let the Nth term of the series be Tn. Sum of the series can be easily found by observing the Nth term of the series:

Tn = {nth term of 2, 3, 4, …} * {nth term of 3, 5, 7, …} * {nth term of 5, 7, 9, …}
Tn = (n + 1) * (2 * n + 1) * (2* n + 3)
Tn = 4n3 + 12n2 + 11n + 3

Sum(Sn) of first n terms can be found by

Sn = ΣTn
Sn = Σ[4n3 + 12n2 + 11n + 3]
Sn = (n / 2) * [2n3 + 12n2 + 25n + 21]

Below is the implementation of the above approach:

## C++

 `// C++ program to find sum of the``// first n terms of the given series``#include ``using` `namespace` `std;` `// Function to return the sum of the``// first n terms of the given series``int` `calSum(``int` `n)``{``    ``// As described in the approach``    ``return` `(n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;``}` `// Driver code``int` `main()``{``    ``int` `n = 3;``    ``cout << calSum(n);``    ``return` `0;``}`

## Java

 `// Java program to find sum of the``// first n terms of the given series``class` `GFG {` `    ``// Function to return the sum of the``    ``// first n terms of the given series``    ``static` `int` `calSum(``int` `n)``    ``{` `        ``// As described in the approach``        ``return` `(n * (``2` `* n * n * n + ``12` `* n * n + ``25` `* n + ``21``)) / ``2``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``3``;``        ``System.out.println(calSum(n));``    ``}``}`

## Python

 `# C++ program to find sum of the``# first n terms of the given series` `# Function to return the sum of the``# first n terms of the given series``def` `calSum(n):``    ` `    ``# As described in the approach``    ``return` `(n``*``(``2` `*` `n``*``n ``*` `n ``+` `12` `*` `n``*``n ``+` `25` `*` `n ``+` `21``))``/``2``;` `# Driver Code``n ``=` `3``print``(calSum(n))`

## C#

 `// C# program to find sum of the``// first n terms of the given series``using` `System;` `class` `GFG {` `    ``// Function to return the sum of the``    ``// first n terms of the given series``    ``static` `int` `calSum(``int` `n)``    ``{` `        ``// As described in the approach``        ``return` `(n * (2 * n * n * n + 12 * n * n + 25 * n + 21)) / 2;``    ``}` `    ``// Driver code``    ``static` `public` `void` `Main()``    ``{``        ``int` `n = 3;``        ``Console.WriteLine(calSum(n));``    ``}``}`

## PHP

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## Javascript

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Output:
`387`

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