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Find n-th term of series 1, 3, 6, 10, 15, 21…
• Difficulty Level : Basic
• Last Updated : 24 Apr, 2018

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
```

## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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

 ` `

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

 ` `

Output :

```10
```

Time Complexity: O(1)

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