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

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  • Last Updated : 06 Dec, 2021
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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)

 


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