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
?>

Javascript

<script>
// Javascript code to generate
// 'Nth' term of this sequence

// Function to generate a fixed number
function nthTerm(N)
{
    let nth = 0;

    //(N^2*(N+1))/2
    nth = parseInt((N * N * (N + 1)) / 2);

    return nth;
}

// Driver Method
let N = 5;

document.write(nthTerm(N));

// This code is contributed by subham348.
</script>

Output:

75

Time Complexity: O(1)

Auxiliary Space: O(1)