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Find n-th term of series 1, 3, 6, 10, 15, 21…
• Difficulty Level : Basic
• Last Updated : 19 Apr, 2021

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 ``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

 ``

## Javascript

 ``

Output:

`10`

Time Complexity of this solution is O(n).

#### Efficient approach :

The pattern in this series is nth term is equal to sum of (n-1)th term and n.
Example :

```n = 2
2nd term equals to sum of 1st 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 ``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

 ``

## Javascript

 ``

Output :

`10`

Time Complexity: O(1)

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