# Find n-th term of series 1, 3, 6, 10, 15, 21…

Given a number n, find the n-th term in the series 1, 3, 6, 10, 15, 21…

Examples:

Input : 3 Output : 6 Input : 4 Output : 10

The given series represent triangular numbers which are sums of natural numbers.

**Naive approach :**

The series basically represents sums of natural numbers. First term is sum of single number. Second term is sum of two numbers, and so on. A simple solution is to add the first n natural numbers.

## C++

`// CPP program to find n-th term of` `// series 1, 3, 6, 10, 15, 21...` `#include <iostream>` `using` `namespace` `std;` `// Function to find the nth term of series` `int` `term(` `int` `n)` `{ ` ` ` `// Loop to add numbers` ` ` `int` `ans = 0;` ` ` `for` `(` `int` `i = 1; i <= n; i++) ` ` ` `ans += i;` ` ` ` ` `return` `ans;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 4;` ` ` `cout << term(n) ;` ` ` `return` `0;` `}` |

## Java

`// Java program to find n-th term of` `// series 1, 3, 6, 10, 15, 21...` `import` `java.io.*;` `class` `GFG {` ` ` ` ` `// Function to find the nth term of series` ` ` `static` `int` `term(` `int` `n)` ` ` `{ ` ` ` `// Loop to add numbers` ` ` `int` `ans = ` `0` `;` ` ` `for` `(` `int` `i = ` `1` `; i <= n; i++)` ` ` `ans += i;` ` ` ` ` `return` `ans;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `n = ` `4` `;` ` ` `System.out.println(term(n));` ` ` `}` `}` `// This code is contributed by Nikita Tiwari.` |

## Python3

`# Python 3 program to find` `# n-th term of` `# series 1, 3, 6, 10, 15, 21...` ` ` `# Function to find the` `# nth term of series` `def` `term(n) :` ` ` `# Loop to add numbers` ` ` `ans ` `=` `0` ` ` `for` `i ` `in` `range` `(` `1` `,n` `+` `1` `) :` ` ` `ans ` `=` `ans ` `+` `i` ` ` ` ` `return` `ans` `# Driver code` `n ` `=` `4` `print` `(term(n))` `# This code is contributed` `# by Nikita Tiwari.` |

## C#

`// C# program to find n-th term of` `// series 1, 3, 6, 10, 15, 21...` `using` `System;` `class` `GFG {` ` ` `// Function to find the nth term` ` ` `// of series` ` ` `static` `int` `term(` `int` `n)` ` ` `{` ` ` ` ` `// Loop to add numbers` ` ` `int` `ans = 0;` ` ` `for` `(` `int` `i = 1; i <= n; i++)` ` ` `ans += i;` ` ` `return` `ans;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 4;` ` ` ` ` `Console.WriteLine(term(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find n-th term of` `// series 1, 3, 6, 10, 15, 21...` `// Function to find the nth` `// term of series` `function` `term(` `$n` `)` `{` ` ` ` ` `// Loop to add numbers` ` ` `$ans` `= 0;` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$ans` `+= ` `$i` `;` ` ` ` ` `return` `$ans` `;` `}` `// Driver code` `$n` `= 4;` `echo` `(term(` `$n` `)) ;` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to find n-th term of` `// series 1, 3, 6, 10, 15, 21...` `// Function to find the nth term of series` `function` `term(n)` `{` ` ` ` ` `// Loop to add numbers` ` ` `let ans = 0;` ` ` `for` `(let i = 1; i <= n; i++) ` ` ` `ans += i;` ` ` ` ` `return` `ans;` `}` `// Driver code` `let n = 4;` `document.write(term(n));` `// This code is contributed by rishavmahato348` `</script>` |

**Output: **

10

Time Complexity of this solution is O(n).

#### Efficient approach :

The pattern in this series is **n ^{th} term is equal to sum of (n-1)^{th} term and n**.

Example :

n = 22^{nd}term equals to sum of 1^{st}term and 2 i.e A2 = A1 + 2 = 1 + 2 = 3 Similarly, A3 = A2 + 3 = 3 + 3 = 6 and so on..

We get:

A(n) = A(n - 1) + n = A(n - 2) + n + (n - 1) = A(n - 3) + n + (n - 1) + (n - 2) . . . = A(1) + 2 + 3... + (n-1) + n A(n) = 1 + 2 + 3 + 4... + (n - 1) + n = n(n + 1) / 2 i.e A(n) is sum of First n natural numbers.

Below is the implementation of the above approach:

## C++

`// CPP program to find the n-th` `// term in series 1 3 6 10 ...` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find nth term` `int` `term(` `int` `n)` `{` ` ` `return` `n * (n + 1) / 2;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 4;` ` ` `cout << term(n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find the n-th` `// term in series 1 3 6 10 ...` `import` `java.io.*;` `class` `Series {` ` ` ` ` `// Function to find nth term` ` ` `static` `int` `term(` `int` `n){` ` ` `return` `n * (n + ` `1` `) / ` `2` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `int` `n = ` `4` `;` ` ` `System.out.println(term(n));` ` ` `}` `}` `// This code is contributed by Chinmoy Lenka` |

## Python

`# Python program to find the Nth` `# term in series 1 3 6 10 ...` `# Function to print nth term` `# of series 1 3 6 10 ....` `def` `term(n):` ` ` `return` `n ` `*` `(n ` `+` `1` `) ` `/` `2` ` ` `# Driver code` `n ` `=` `4` `print` `term(n)` |

## C#

`// C# program to find the n-th` `// term in series 1 3 6 10 ...` `using` `System;` `class` `GFG {` ` ` `// Function to find nth term` ` ` `static` `int` `term(` `int` `n)` ` ` `{` ` ` `return` `n * (n + 1) / 2;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 4;` ` ` ` ` `Console.WriteLine(term(n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find the n-th` `// term in series 1 3 6 10 ...` `// Function to find nth term` `function` `term(` `$n` `)` `{` ` ` `return` `$n` `* (` `$n` `+ 1) / 2;` `}` `// Driver code` `$n` `= 4;` `echo` `(term(` `$n` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to find the n-th` `// term in series 1 3 6 10 ...` `// Function to find nth term` `function` `term(n)` `{` ` ` `return` `parseInt(n * (n + 1) / 2);` `}` `// Driver code` `let n = 4;` `document.write(term(n));` `// This code is contributed by subhammahato348.` `</script>` |

**Output :**

10

**Time Complexity:** O(1)