Find Nth term of the series 1, 6, 18, 40, 75, ....

Given a number n, the task is to find the n-th term in series 1, 6, 18, 40, 75, …

Example:

Input: N = 2
Output: 6
Explanation:
2nd term = (2^2*(2+1))/2
         = 6

Input: N = 5
Output: 75
Explanation:
5th term = (5^2*(5+1))/2
         = 75

Approach:

Nth term = (N^2*(N+1))/2

Implementation of the above approach is given below:

C++

// CPP code to generate 
// 'Nth' term of this sequence 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to generate a fixed number 
int nthTerm(int N) 
{ 
    int nth = 0; 
  
    //(N^2*(N+1))/2 
    nth = (N * N * (N + 1)) / 2; 
  
    return nth; 
} 
  
// Driver Method 
int main() 
{ 
    int N = 5; 
  
    cout << nthTerm(N) << endl; 
  
    return 0; 
} 

Java

// Java code to generate 
// 'Nth' term of this sequence 
  
class GFG { 
  
    // Function to generate a fixed number 
    public static int nthTerm(int N) 
    { 
        int nth = 0; 
  
        //(N^2*(N+1))/2 
        nth = (N * N * (N + 1)) / 2; 
  
        return nth; 
    } 
  
    // Driver Method 
    public static void main(String[] args) 
    { 
        int N = 5; 
  
        System.out.println(nthTerm(N)); 
    } 
    // This code is contributed by 29AjayKumar 
} 

Python3

# python program to find out'Nth' term of this sequence  
  
# Function to generate a fixed number 
def nthTerm(N): 
    nth = 0
    nth = (N * N * (N + 1))//2
    return nth 
  
# Driver code 
N = 5
print(nthTerm(N)) 
  
# This code is contributed by Shrikant13 

C#

// C# code to generate 
// 'Nth' term of this sequence 
  
using System; 
public class GFG { 
  
    // Function to generate a fixed number 
    public static int nthTerm(int N) 
    { 
        int nth = 0; 
  
        //(N^2*(N+1))/2 
        nth = (N * N * (N + 1)) / 2; 
  
        return nth; 
    } 
  
    // Driver Method 
    public static void Main(string[] args) 
    { 
        int N = 5; 
  
        Console.WriteLine(nthTerm(N)); 
    } 
} 
  
// This code is contributed by Shrikant13 

PHP

<?php 
// PHP code to generate 
// 'Nth' term of this sequence 
  
// Function to generate a fixed number 
function nthTerm($N) 
{ 
    $nth = 0; 
  
    // (N^2*(N+1))/2 
    $nth = ($N * $N * ($N + 1)) / 2; 
  
    return $nth; 
} 
  
// Driver Code 
$N = 5; 
  
echo nthTerm($N); 
  
// This code is contributed 
// by chandan_jnu 
?> 

Output:

Time Complexity: O(1)

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My Personal Notes

Find Nth term of the series 1, 6, 18, 40, 75, ….

C++

Java

Python3

C#

PHP

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