Find N-th term in the series 0, 4, 18, 48, 100 …

Given a series 0, 4, 18, 48, 100 . . .  and an integer N, the task is to find the N-th term of the series.

Examples:

Input: N = 4
Output: 48
Explanation: As given in the sequence we can see that 4th term is 48

Input: N = 6
Output: 180

Approach: Consider the below observation:

For N = 2, the 2nd term is 4, which can be represented as 8 – 4, i.e. 2³ – 2²

For N = 3, the 3rd term is 18, which can be represented as 27 – 9, i.e. 3³ – 3²

For N = 4, the 4th term is 18, which can be represented as 27 – 9, i.e. 4³ – 4²

.

.

.

Similarly, The N-th term of this series can be represented as N³ – N²

So for any N, find the square of that N and subtract it from the cube of the number.

Below is the implementation of the above approach:

C++

// C++ code to find Nth term of series
// 0, 4, 18, ...

#include <bits/stdc++.h>
using namespace std;

// Function to find N-th term
// of the series
int getNthTerm(int N)
{
    // (pow(N, 3) - pow(N, 2))
    return (N * N * N) - (N * N);
}

// Driver Code
int main()
{
    int N = 4;

    // Get the 8th term of the series
    cout << getNthTerm(N);
    return 0;
}

Java

// Java code to find Nth term of series
// 0, 4, 18, ...
class GFG
{

    // Function to find N-th term
    // of the series
    public static int getNthTerm(int N)
    {

        // (pow(N, 3) - pow(N, 2))
        return (N * N * N) - (N * N);
    }

    // Driver Code
    public static void main(String args[])
    {
        int N = 4;

        // Get the 8th term of the series
        System.out.println(getNthTerm(N));
    }
}

// This code is contributed by gfgking

Python3

# Python code to find Nth term of series
# 0, 4, 18, ...

# Function to find N-th term
# of the series
def getNthTerm(N):

    # (pow(N, 3) - pow(N, 2))
    return (N * N * N) - (N * N);

# Driver Code
N = 4;

# Get the 8th term of the series
print(getNthTerm(N));

# This code is contributed by gfgking

C#

// C# code to find Nth term of series
// 0, 4, 18, ...

using System;
class GFG {
    // Function to find N-th term
    // of the series
    public static int getNthTerm(int N) {
        // (pow(N, 3) - pow(N, 2))
        return (N * N * N) - (N * N);
    }

    // Driver Code
    public static void Main() {
        int N = 4;

        // Get the 8th term of the series
        Console.Write(getNthTerm(N));
    }
}

// This code is contributed by gfgking

Javascript

<script>
// Javascript code to find Nth term of series
// 0, 4, 18, ...



// Function to find N-th term
// of the series
function getNthTerm(N) {
    // (pow(N, 3) - pow(N, 2))
    return (N * N * N) - (N * N);
}

// Driver Code

let N = 4;

// Get the 8th term of the series
document.write(getNthTerm(N));
// This code is contributed by gfgking
</script>

Output

48

Time complexity: O(1)
Auxiliary space: O(1)