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

• Last Updated : 07 Aug, 2022

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```

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++

 `// C++ 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

 `# 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

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## Javascript

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Output:

`91`

Time Complexity: O(1)

Auxiliary Space: O(1)

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