Find nth term of 0, 9, 24, 45, . . . .

Given a natural number N, the task is to find the Nth term of the series 

0, 9, 24, 45, . . . .till N terms

Examples:

Input: N = 4 
Output: 45

Input: N = 6
Output: 105

Approach:

From the given series, find the formula for Nth term-

1st term = 3 * 1 * 1 – 3 = 0 

2nd term = 3 * 2 * 2 – 3 = 9 

3rd term = 3 * 3 * 3 – 3 = 24

4th term = 3 * 4 * 4 – 3 = 45

.

.

Nth term = 3 * N * N – 3

The Nth term of the given series can be generalized as-

T_N = 3 * N * N – 3

Illustration:

Input: N = 6
Output: 105
Explanation:
T_N = 3 * N * N – 3
     = 3 * 6 * 6 – 3
     = 108 – 3
     = 105

Below is the implementation of the above approach-

C++

// C++ program to implement
// the above approach
#include <iostream>
using namespace std;

// Function to return nth
// term of the series
int nth_Term(int n)
{
    return 3 * n * n - 3;
}

// Driver code
int main()
{
    // Value of N
    int N = 6;

    // Invoke function to find
    // Nth term
    cout << nth_Term(N) <<
            endl;
    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;
public class GFG
{

  // Function to return nth
  // term of the series
  static int nth_Term(int n)
  {
    return 3 * n * n - 3;
  }

  // Driver code
  public static void main(String args[])
  {

    // Value of N
    int N = 6;

    // Invoke function to find
    // Nth term
    System.out.println(nth_Term(N));
  }
}

// This code is contributed by Samim Hossain Mondal.

Python3

# Python code for the above approach

# Function to return nth
# term of the series
def nth_Term(n):
    return 3 * n * n - 3;

# Driver code

# Value of N
N = 6;

# Invoke function to find
# Nth term
print(nth_Term(N))

# This code is contributed by gfgking

C#

// C# program to implement
// the above approach
using System;
class GFG
{

// Function to return nth
// term of the series
static int nth_Term(int n)
{
    return 3 * n * n - 3;
}

// Driver code
public static void Main()
{
    // Value of N
    int N = 6;

    // Invoke function to find
    // Nth term
    Console.WriteLine(nth_Term(N));
}
}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
      // JavaScript code for the above approach

      // Function to return nth
      // term of the series
      function nth_Term(n) {
          return 3 * n * n - 3;
      }

      // Driver code

      // Value of N
      let N = 6;

      // Invoke function to find
      // Nth term
      document.write(nth_Term(N) + '<br>')


     // This code is contributed by Potta Lokesh
  </script>

Output

105

Time Complexity: O(1)

Auxiliary Space: O(1)