Program to find Nth term of series 1, 6, 17, 34, 56, 86, 121, 162, …….

Given a number N. The task is to write a program to find the Nth term of the below series:

1, 6, 17, 34, 56, 86, 121, 162, …..(N Terms)

Examples:

Input: N = 4
Output: 34
For N = 4
4th Term = ( 3 * 4 * 4 - 4 * 4 + 2) 
         = 34

Input: N = 10
Output: 261

Approach: The generalized Nth term of this series: 

Below is the required implementation: 

C++

// C++ program to find the N-th term of the series:
// 1, 6, 17, 34, 56, 86, 121, 162, .....
#include <iostream>
#include <math.h>
using namespace std;

// calculate Nth term of series
int nthTerm(int n)
{
    return 3 * pow(n, 2) - 4 * n + 2;
}

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

    cout << nthTerm(N) << endl;

    return 0;
}

Java

// Java program to find the N-th term of the series:
// 1, 6, 17, 34, 56, 86, 121, 162, .....

public class GFG {

    // calculate Nth term of series
    static int nthTerm(int n)
    {
        return 3 * (int) Math.pow(n, 2) - 4 * n + 2;
    }

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

       System.out.println(nthTerm(N));

    }
    // This Code is contributed by ANKITRAI1
}

Python3

# Python program to find the
# N-th term of the series:
# 1, 6, 17, 34, 56, 86, 121, 162, .....

# calculate Nth term of series
def nthTerm(n):

    return 3 * pow(n, 2) - 4 * n + 2

# Driver code
N = 4
print(nthTerm(N))

# This code is contributed by
# Sanjit_Prasad

C#

// C# program to find the
// N-th term of the series:
// 1, 6, 17, 34, 56, 86, 121, 162, .....
using System;
class GFG
{

// calculate Nth term of series
static int nthTerm(int n)
{
    return 3 * (int) Math.Pow(n, 2) -
                         4 * n + 2;
}

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

    Console.Write(nthTerm(N));
}
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP program to find the
// N-th term of the series:
// 1, 6, 17, 34, 56, 86, 121, 162, .....

// calculate Nth term of series
function nthTerm($n)
{
    return 3 * pow($n, 2) -
           4 * $n + 2;
}

// Driver code
$N = 4;

echo nthTerm($N)."\n";

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>
// JavaScript program to find the N-th term of the series:
// 1, 6, 17, 34, 56, 86, 121, 162, .....

// calculate Nth term of series
function nthTerm(n)
{
    return 3 * Math.pow(n, 2) - 4 * n + 2;
}

// Driver code
let N = 4;

     document.write( nthTerm(N) );

// This code contributed by gauravrajput1

</script>

Output:

34

Time Complexity: O(1), since there is no loop or recursion.

Space Complexity: O(1) since using constant variables