Program to find the Nth term of series 0, 4, 14, 30, 51, 80, 114, 154, 200, …

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

0, 4, 14, 30, 51, 80, 114, 154, 200, …(N Terms)

Examples:

Input: N = 4
Output: 82
For N = 4
4th Term = ( 4 * 4 - 2 * 4 + 2) 
         = 10

Input: N = 10
Output: 122

Approach: The generalized Nth term of this series: 

Below is the required implementation: 

C++

// CPP program to find the N-th term of the series:
// 5, 10, 17, 26, 37, 50, 65, 82, ...
#include <iostream>
#include <math.h>
using namespace std;

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

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

    cout << nthTerm(N);

    return 0;
}

Java

// Java program to find the N-th term of the series:
// 5, 10, 17, 26, 37, 50, 65, 82, ...
import java.util.*;

class solution
{

// calculate Nth term of series
static int nthTerm(int n)
{

    //return the total sum
    return (int)Math.pow(n, 2) - 2 * n + 2;
}

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

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

}

}

Python3

# Python3 program to find the N-th
# term of the series:
# 0, 4, 14, 30, 51, 80, 114, 154, 200, …

# from math lib. import everything
from math import *

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

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


# Driver code
if __name__ == "__main__" :

    N = 4
    print(nthTerm(N))

# This code is contributed by
# ANKITRAI1

C#

// C# program to find the
// N-th term of the series:
// 5, 10, 17, 26, 37, 50, 65, 82, ...
using System;

class GFG
{

// calculate Nth term of series
public static int nthTerm(int n)
{

    // return the total sum
    return (int)Math.Pow(n, 2) -
                    2 * n + 2;
}

// Driver Code
public static void Main(string[] arr)
{
    int N = 4;

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

// This code is contributed
// by Shrikant13

PHP

<?php
// PHP program to find the
// N-th term of the series:
// 5, 10, 17, 26, 37, 50, 65, 82, ...

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

// Driver Code
$N = 4;

echo nthTerm($N);

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

Javascript

<script>
// JavaScript program to find the N-th term of the series:
// 5, 10, 17, 26, 37, 50, 65, 82, ...

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

    let N = 4;
   document.write( nthTerm(N) );

// This code contributed by aashish1995

</script>

Output:

10

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

Space Complexity: O(1) since using constant variables