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++

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// 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;
}

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Java

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// 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
}

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Python3

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# 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

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C#

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// 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

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PHP

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<?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
?>

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Output:

75

Time Complexity: O(1)



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