Find the Nth term of the series 2 + 6 + 13 + 23 + . . .

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Given an integer N. The task is to write a program to find the Nth term of the given series:

2 + 6 + 13 + 23 + …

Examples:

Input : N = 5
Output : 36

Input : N = 10
Output : 146

Refer the article on How to find Nth term of series to know idea behind finding Nth term of any given series.
The generalized N-th term of given series is:
$t_{n} = \frac{3n^{2}-n+2}{2}$
Below is the implementation of above approach:

C++

//CPP program to find Nth term of the series
// 2 + 6 + 13 + 23 + 36 + ...
#include<bits/stdc++.h>
using namespace std;
 
// calculate Nth term of given series
int Nth_Term(int n)
{
     
return (3 * pow(n, 2) - n + 2) / (2);
 
}
 
// Driver code
int main()
{
 
int N = 5;
cout<<Nth_Term(N)<<endl;
 
}

Java

//Java program to find Nth term of the series
// 2 + 6 + 13 + 23 + 36 + ...
import java.io.*;
 
class GFG {
 
// calculate Nth term of given series
static int Nth_Term(int n)
{
     
return (int)(3 * Math.pow(n, 2) - n + 2) / (2);
 
}
 
// Driver code
 
    public static void main (String[] args) {
    int N = 5;
    System.out.println(Nth_Term(N));
    }
}
// This code is contributed by anuj_67..

Python3

# Python program to find Nth term of the series
# 2 + 6 + 13 + 23 + 36 + ...
 
# calculate Nth term of given series
def Nth_Term(n):
    return (3 * pow(n, 2) - n + 2) // (2)
 
# Driver code
N = 5
print(Nth_Term(N))

C#

// C# program to find Nth term of the series
// 2 + 6 + 13 + 23 + 36 + ...
 
class GFG 
{
 
// calculate Nth term of given series
static int Nth_Term(int n)
{
     
    return (int)(3 * System.Math.Pow(n, 2) -
                              n + 2) / (2);
}
 
// Driver code
static void Main ()
{
    int N = 5;
    System.Console.WriteLine(Nth_Term(N));
}
}
 
// This code is contributed by mits

PHP

<?php
// PHP program to find 
// Nth term of the series
// 2 + 6 + 13 + 23 + 36 + ...
 
// calculate Nth term of given series
function Nth_Term($n)
{
    return (3 * pow($n, 2) - $n + 2) / (2);
}
 
// Driver code
$N = 5;
echo (Nth_Term($N));
 
// This code is contributed 
// by Sach_Code
?>

Javascript

<script>
 
// java script program to find
// Nth term of the series
// 2 + 6 + 13 + 23 + 36 + ...
 
// calculate Nth term of given series
function Nth_Term(n)
{
    return (3 * Math.pow(n, 2) - n + 2) / (2);
}
 
// Driver code
let N = 5;
document.write (Nth_Term(N));
 
// This code is contributed 
// by bobby
</script>

Output:

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

Auxiliary Space: O(1), since no extra space has been taken.

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