Find nth term of series 3, 11, 31, 69, . . . . .

Given an integer N, the task is to find the Nth term of the series 

3, 11, 31, 69, . . . . . till Nth term.

Examples:

Input: N = 3 
Output: 31

Input: N = 6
Output: 223

Approach:

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

1st term = 1 ^ 3 + (1 + 1) = 3

2nd term = 2 ^ 3 + (2 + 1) = 11

3rd term = 3 ^ 3 + (3 + 1) = 31

4th term = 4 ^ 3 + (4 + 1) = 69

.

.

Nth term = n  ^ 3 + (n + 1)

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

T_N = n  ^ 3 + (n + 1)

Illustration:

Input: N = 5
Output: 131
Explanation:
T_N = n  ^ 3 + (n + 1)   
     = 5 ^ 3 + (5 + 1)    
     = 131

Below is the implementation of the above approach-

C++

// C++ program to find nth
// term of the series
#include <iostream>
using namespace std;

// Function to return nth
// term of the series
int find_nth_Term(int n)
{
    return n * n * n + (n + 1);
}

// Driver code
int main()
{
    // Find given nth term
    int n = 5;

    // Function call
    cout << find_nth_Term(n) << endl;
    return 0;
}

Java

// Java code for the above approach
import java.io.*;

class GFG {

  // Function to return nth
  // term of the series
  static int find_nth_Term(int n)
  {
    return n * n * n + (n + 1);
  }

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

    // Find given nth term
    int n = 5;

    // Function call
    System.out.println(find_nth_Term(n));
  }
}

// This code is contributed by Potta Lokesh

Python

# Python program to find nth
# term of the series

# Function to return nth
# term of the series
def find_nth_Term(n):

    return n * n * n + (n + 1)

# Driver code

# Find given nth term
n = 5

# Function call
print(find_nth_Term(n))

# This code is contributed by Samim Hossain Mondal.

C#

// C# program to find nth
// term of the series
using System;
class GFG
{

  // Function to return nth
  // term of the series
  static int find_nth_Term(int n)
  {
    return n * n * n + (n + 1);
  }

  // Driver code
  public static int Main()
  {

    // Find given nth term
    int n = 5;

    // Function call
    Console.WriteLine(find_nth_Term(n));
    return 0;
  }
}

// This code is contributed by Taranpreet

Javascript

<script>
// Javascript program to find nth
// term of the series

// Function to return nth
// term of the series
function find_nth_Term(n)
{
    return n * n * n + (n + 1);
}

// Driver code
// Find given nth term
let n = 5;

// Function call
document.write(find_nth_Term(n))

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

Output

131

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.