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

• Difficulty Level : Basic
• Last Updated : 07 Jun, 2022

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: O(N), as we are using a loop to traverse N times.

Auxiliary Space: O(1), as we are not using any extra space.

#### 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), as we are not using any loop or recursion to traverse.

Auxiliary Space: O(1), as we are not using any extra space.

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