Find the Nth term of the series 3,10,21,36,55…

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

3, 10, 21, 36, 55…till N terms

Examples:

Input: N = 4
Output: 36

Input: N = 6
Output: 78

Approach:

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

1st term = 1 * ( 2(1) + 1 ) = 3

2nd term = 2 * ( 2(2) + 1 ) = 10

3rd term = 3 * ( 2(3) + 1 ) = 21

4th term = 4 * ( 2(4) + 1 ) = 36

.

.

Nth term = N * ( 2(N) + 1 ) 

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

T_N =  N * ( 2(N) + 1 ) 

Illustration:

Input: N = 10
Output: 210
Explanation:
T_N = N * ( 2(N) + 1 )  
     = 10 * ( 2(10) + 1 ) 
     = 210

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(int n)
{
    return n * (2 * n + 1);
}

// Driver code
int main()
{
    int N = 10;
    cout << nTh(N) << endl;
    return 0;
}

C

// C program to implement
// the above approach
#include <stdio.h>

// Function to return
// Nth term of the series
int nTh(int n)
{
    return n * (2 * n + 1);
}

// Driver code
int main()
{
    // Value of N
    int N = 10;
    printf("%d", nTh(N));
    return 0;
}

Java

// Java program to implement
// the above approach
import java.io.*;

class GFG {
    // Driver code
    public static void main(String[] args)
    {
        int N = 10;
        System.out.println(nTh(N));
    }

    // Function to return
    // Nth term of the series
    public static int nTh(int n)
    {
        return n * (2 * n + 1);
    }
}

Python

# Python program to implement
# the above approach

# Function to return
# Nth term of the series
def nTh(n):

    return n * (2 * n + 1)

# Driver code

N = 10
print(nTh(N))

# This code is contributed by Samim Hossain Mondal.

C#

using System;

public class GFG
{

  // Function to return
  // Nth term of the series
  public static int nTh(int n)
  {
    return n * (2 * n + 1);
  }
  static public void Main (){

    // Code
    int N = 10;
    Console.Write(nTh(N));
  }
}

// This code is contributed by Potta Lokesh

Javascript

<script>
    // JavaScript code for the above approach

    // Function to return
    // Nth term of the series
    function nTh(n) {
        return n * (2 * n + 1);
    }

    // Driver code
    let N = 10;
    document.write(nTh(N) + '<br>');

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

Output

210

Time Complexity: O(1) // since no loop is used the algorithm takes up constant time to perform the operations

Auxiliary Space: O(1) // since no extra array is used so the space taken by the algorithm is constant