# Program to find Nth term of series 7, 21, 49, 91, 147, 217, ……

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

Input: N = 10
Output: 636
```

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

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 = (12) – (1-1)
3 = (22) – (2-1)
7 = (32) – (3-1)
13 = (42) – (4-1)
21 = (52) – (5-1)
.
.
.
n-th term = (n2) – (n-1)

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

```N-th term = 7 * ((n2) - (n-1))
= 7 * (n2 - 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 ` `#include ` `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

 `# 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)) `

## 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

 `  `

Output:

```91
```

Time Complexity: O(1)

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