Find Nth term of the series 5, 13, 25, 41, 61…

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

5, 13, 25, 41, 61...

**Examples:**

Input :3Output :25 For N = 3 Nth term = 3*3 + (3+1)*(3+1) = 25Input :5Output :61

On observing carefully, the Nth term of the given series can be generalised as:

Nth term = N^{2}+ (N+1)^{2}

Below is the implementation of the above approach:

## C++

`// CPP program to find N-th term of the series: ` `// 5, 13, 25, 41, 61... ` `#include <iostream> ` `using` `namespace` `std; ` ` ` `// calculate Nth term of series ` `int` `nthTerm(` `int` `N) ` `{ ` ` ` `return` `N * N + (N + 1) * (N + 1); ` `} ` ` ` `// Driver Function ` `int` `main() ` `{ ` ` ` `int` `N = 3; ` ` ` ` ` `cout << nthTerm(N); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to calculate Nth term of ` `// the series: 5, 13, 25, 41, 61... ` ` ` `import` `java.io.*; ` ` ` `class` `Nth { ` ` ` `public` `static` `int` `nthTerm(` `int` `N) ` ` ` `{ ` ` ` `// By using above formula ` ` ` `return` `N * N + (N + ` `1` `) * (N + ` `1` `); ` ` ` `} ` ` ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `N = ` `3` `; ` `// Nth term is 25 ` ` ` ` ` `// call and print Nth term ` ` ` `System.out.println(nthTerm(N)); ` ` ` `} ` `} ` |

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## Python 3

`# Python 3 program to find ` `# N-th term of the series: ` `# 5, 13, 25, 41, 61... ` ` ` `# Function to calculate ` `# Nth term of series ` `def` `nthTerm(N) : ` ` ` `return` `N ` `*` `N ` `+` `(N ` `+` `1` `) ` `*` `(N ` `+` `1` `) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `N ` `=` `3` ` ` ` ` `# function calling ` ` ` `print` `(nthTerm(N)) ` ` ` `# This code is contributed ` `# by ANKITRAI1 ` |

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## C#

`// C# program to calculate Nth term of ` `// the series: 5, 13, 25, 41, 61... ` `using` `System; ` ` ` `class` `GFG ` `{ ` `public` `static` `int` `nthTerm(` `int` `N) ` `{ ` ` ` `// By using above formula ` ` ` `return` `N * N + (N + 1) * (N + 1); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `N = 3; ` `// Nth term is 25 ` ` ` ` ` `// call and print Nth term ` ` ` `Console.Write(nthTerm(N)); ` `} ` `} ` ` ` `// This code is contributed ` `// by ChitraNayal ` |

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## PHP

`<?php ` `// PHP program to find N-th ` `// term of the series: ` `// 5, 13, 25, 41, 61... ` ` ` `// calculate Nth term of series ` `function` `nthTerm(` `$N` `) ` `{ ` ` ` `return` `$N` `* ` `$N` `+ (` `$N` `+ 1) * ` ` ` `(` `$N` `+ 1); ` `} ` ` ` `// Driver Code ` `$N` `= 3; ` ` ` `echo` `nthTerm(` `$N` `); ` ` ` `// This code is contributed ` `// by ChitraNayal ` `?> ` |

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**Output:**

25

**Time Complexity:** O(1)