Related Articles

Related Articles

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 

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)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up
Recommended Articles
Page :