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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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.

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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 +
       
    return ans
  
  
# Driver code
n = 4
print(term(n))
  
# This code is contributed
# by Nikita Tiwari.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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.
?>

chevron_right


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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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)

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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.
?>

chevron_right


Output :

10

Time Complexity: O(1)



My Personal Notes arrow_drop_up

Striver(underscore)79 at Codechef and codeforces D

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : jit_t