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++

`// C++ 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;` `}` |

## 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));` `}` `}` |

## Python3

`# Python3 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))` |

## 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` |

## 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` `?>` |

## Javascript

`<script>` `// Javascript program to find the N-th term` `// of the series:` `// 7, 21, 49, 91, 146, 217, 301, 399, ...` `// Calculate Nth term of series` `function` `nthTerm(n)` `{` ` ` `return` `7 * Math.pow(n, 2) - 7 * n + 7;` `}` `// Driver code` `let N = 4;` `document.write(nthTerm(N));` `// This code is contributed by Surbhi Tyagi.` `</script>` |

**Output:**

91

**Time Complexity:** O(1)

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