Program to find Nth term of the series 3 , 5 , 21 , 51 , 95 , …

Given a number N, the task is to find the Nth term of this series:

3, 5, 21, 51, 95, ….

**Examples:**

Input:N = 4Output:51Explanation:Nth term = (7 * pow(N, 2) - 19 * N + 15) = (7 * pow(4, 2) - 19 * 4 + 15) = 51Input:N = 10Output:525

**Approach:**

The Nth term of the given series can be generalized as:

Below is the implementation of the above approach:

## C++

`// CPP program to find N-th term of the series: ` `// 3, 5, 21, 51, 95,... ` ` ` `#include <iostream> ` `#include <math.h> ` `using` `namespace` `std; ` ` ` `// calculate Nth term of series ` `int` `getNthTerm(` `long` `long` `int` `N) ` `{ ` ` ` `// Return Nth term ` ` ` `return` `(7 * ` `pow` `(N, 2) - 19 * N + 15); ` `} ` ` ` `// driver code ` `int` `main() ` `{ ` ` ` `// declaration of number of terms ` ` ` `long` `long` `int` `N = 4; ` ` ` ` ` `// Get the Nth term ` ` ` `cout << getNthTerm(N); ` ` ` ` ` `return` `0; ` `} ` |

## Java

`// Java program to find N-th term of the series: ` `// 3, 5, 21, 51, 95,... ` `import` `java.util.*; ` ` ` `class` `solution ` `{ ` `static` `long` `getNthTerm(` `long` `N) ` `{ ` `// Return Nth term ` ` ` `return` `(` `7` `*(` `int` `) Math.pow(N, ` `2` `) - ` `19` `* N + ` `15` `); ` `} ` ` ` `//Driver program ` `public` `static` `void` `main(String arr[]) ` `{ ` `// declaration of number of terms ` ` ` `long` `N = ` `4` `; ` ` ` ` ` `// Get the Nth term ` ` ` `System.out.println(getNthTerm(N)); ` `} ` `} ` |

## Python3

`# Python3 program to find N-th term ` `# of the series: ` `# 3, 5, 21, 51, 95,... ` ` ` `# calculate Nth term of series ` `def` `getNthTerm(N): ` ` ` ` ` `#Return Nth term ` ` ` `return` `(` `7` `*` `pow` `(N, ` `2` `) ` `-` `19` `*` `N ` `+` `15` `) ` ` ` `#Driver code ` `if` `__name__` `=` `=` `'__main__'` `: ` ` ` `#declaration of number of terms ` ` ` `N ` `=` `4` ` ` `#Get the Nth term ` ` ` `print` `(getNthTerm(N)) ` ` ` `#this code is contributed by Shashank_Sharma ` |

## C#

`// C# program to find ` `// N-th term of the series: ` `// 3, 5, 21, 51, 95,... ` `using` `System; ` ` ` `class` `GFG ` `{ ` `static` `long` `getNthTerm(` `long` `N) ` `{ ` ` ` `// Return Nth term ` ` ` `return` `(7 *(` `int` `) Math.Pow(N, 2) - ` ` ` `19 * N + 15); ` `} ` ` ` `// Driver Code ` `static` `public` `void` `Main () ` `{ ` ` ` ` ` `// declaration of number ` ` ` `// of terms ` ` ` `long` `N = 4; ` ` ` ` ` `// Get the Nth term ` ` ` `Console.Write(getNthTerm(N)); ` `} ` `} ` ` ` `// This code is contributed by Raj ` |

## PHP

`<?php ` `// PHP program to find ` `// N-th term of the series: ` `// 3, 5, 21, 51, 95,... ` ` ` `// calculate Nth term of series ` `function` `getNthTerm(` `$N` `) ` `{ ` ` ` `// Return Nth term ` ` ` `return` `(7 * pow(` `$N` `, 2) - ` ` ` `19 * ` `$N` `+ 15); ` `} ` ` ` `// Driver code ` ` ` `// declaration of number ` `// of terms ` `$N` `= 4; ` ` ` `// Get the Nth term ` `echo` `getNthTerm(` `$N` `); ` ` ` `// This code is contributed ` `// by anuj_67 ` `?> ` |

**Output:**

51

**Time Complexity:** O(1)

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