Given a number N. The task is to write a program to find the Nth term of the below series:

7, 21, 49, 91, 147, 217, 301, 399, …(N Terms)

**Examples**:

Input: N = 4Output: 91 For N = 4 4th Term = ( 7 * 4 * 4 - 7 * 4 + 7) = 91Input: N = 10Output: 636

Given series is:

7, 21, 49, 91, 147, 217, 301, 399, …..

On taking 7 commons from all of the terms, we get:

7 * (1, 3, 7, 13, 21, 31,…..), …..

Now, for the inner-series: **1,3,7,13,21,… **

On careful observation we can express the terms of above series as:

1 = (1^{2}) – (1-1)

3 = (2^{2}) – (2-1)

7 = (3^{2}) – (3-1)

13 = (4^{2}) – (4-1)

21 = (5^{2}) – (5-1)

.

.

.

n-th term = (n^{2}) – (n-1)

Therefore, the n-th term of the actual series will be:

N-th term = 7 * ((n^{2}) - (n-1)) = 7 * (n^{2}- n + 1)

Below is the implementation of the above approach:

## C++

`// CPP program to find the N-th term of the series: ` `// 7, 21, 49, 91, 146, 217, 301, 399, ... ` `#include <iostream> ` `#include <math.h> ` `using` `namespace` `std; ` ` ` `// calculate Nth term of series ` `int` `nthTerm(` `int` `n) ` `{ ` ` ` `return` `7 * ` `pow` `(n, 2) - 7 * n + 7; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `N = 4; ` ` ` ` ` `cout << nthTerm(N); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find the N-th term of the series: ` `// 7, 21, 49, 91, 146, 217, 301, 399, ... ` ` ` `// calculate Nth term of series ` `import` `java.util.*; ` ` ` `class` `solution ` `{ ` ` ` `//Function to find the nth term of the series ` `static` `int` `nthTerm(` `int` `n) ` `{ ` ` ` `return` `7` `* (` `int` `)Math.pow(n, ` `2` `) - ` `7` `* n + ` `7` `; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String arr[]) ` `{ ` ` ` `int` `N = ` `4` `; ` ` ` ` ` `System.out.println(nthTerm(N)); ` ` ` `} ` ` ` `} ` |

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## Python3

`# Python 3 program to find the N-th term of the series: ` `# 7, 21, 49, 91, 146, 217, 301, 399, ... ` ` ` ` ` `# calculate Nth term of series ` `def` `nthTerm( n): ` ` ` ` ` `return` `7` `*` `pow` `(n, ` `2` `) ` `-` `7` `*` `n ` `+` `7` ` ` ` ` `# Driver code ` `N ` `=` `4` ` ` `print` `(nthTerm(N)) ` |

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## C#

`// C# program to find the ` `// N-th term of the series: ` `// 7, 21, 49, 91, 146, 217, 301, 399, ... ` `using` `System; ` ` ` `// calculate Nth term of series ` `class` `GFG ` `{ ` ` ` `// Function to find the Nth ` `// term of the series ` `static` `int` `nthTerm(` `int` `n) ` `{ ` ` ` `return` `7 * (` `int` `)Math.Pow(n, 2) - 7 * n + 7; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `N = 4; ` ` ` ` ` `Console.WriteLine(nthTerm(N)); ` `} ` `} ` ` ` `// This code is contributed ` `// by Akanksha Rai ` |

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## PHP

`<?php ` `// PHP program to find the ` `// N-th term of the series: ` `// 7, 21, 49, 91, 146, 217, 301, 399, ... ` `function` `Sum_upto_nth_Term(` `$n` `) ` `{ ` ` ` `$r` `= 7 * pow(` `$n` `, 2) - 7 * ` `$n` `+ 7; ` ` ` `echo` `$r` `; ` `} ` ` ` `// Driver code ` `$N` `= 4; ` `Sum_upto_nth_Term(` `$N` `); ` ` ` `// This code is contributed ` `// by Sanjit_Prasad ` `?> ` |

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**Output:**

91

**Time Complexity:** O(1)

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