n-th term in series 2, 12, 36, 80, 150....

Given a series 2, 12, 36, 80, 150.. Find the n-th term of the series.
Examples :

Input : 2
Output : 12

Input : 4
Output : 80

If we take a closer look, we can notice that series is sum of squares and cubes of natural numbers (1, 4, 9, 16, 25, .....) + (1, 8, 27, 64, 125, ....).
Therefore n-th number of the series is n^2 + n^3

C++

// CPP program to find n-th term of
// the series  2, 12, 36, 80, 150, ..
#include <iostream>
using namespace std;

// Returns n-th term of the series
// 2, 12, 36, 80, 150
int nthTerm(int n)
{
    return (n * n) + (n * n * n);
}

// driver code
int main()
{
    int n = 4;
    cout << nthTerm(n);
    return 0;
}

Java

//java program to find n-th term of
// the series 2, 12, 36, 80, 150, ..
import java.util.*;

class GFG
{
    // Returns n-th term of the series
    // 2, 12, 36, 80, 150
    public static int nthTerm(int n)
    {
        return (n * n) + (n * n * n);
    }
    
    // Driver code 
    public static void main(String[] args)
    {
        int n = 4;
        System.out.print(nthTerm(n));
    }
}

// This code is contributed by rishabh_jain

Python3

# Python3 code to find n-th term of
# the series 2, 12, 36, 80, 150, ..

# Returns n-th term of the series
# 2, 12, 36, 80, 150
def nthTerm( n ):
    return (n * n) + (n * n * n)

# driver code
n = 4
print( nthTerm(n))

# This code is contributed 
# by "Sharad_Bhardwaj".

// C# program to find n-th term of
// the series 2, 12, 36, 80, 150, ..
using System;

class GFG
{
    // Returns n-th term of the series
    // 2, 12, 36, 80, 150
    public static int nthTerm(int n)
    {
        return (n * n) + (n * n * n);
    }
    
    // Driver code 
    public static void Main()
    {
        int n = 4;
        Console.WriteLine(nthTerm(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find n-th term of
// the series 2, 12, 36, 80, 150, ..

// Returns n-th term of the series
// 2, 12, 36, 80, 150
function nthTerm($n)
{
    return ($n * $n) + ($n * $n * $n);
}

// driver code
$n = 4;
echo(nthTerm($n));

// This code is contributed by Ajit.
?>

JavaScript

<script>
// Javascript program to find n-th term of
// the series 2, 12, 36, 80, 150, ..

// Returns n-th term of the series
// 2, 12, 36, 80, 150
function nthTerm(n)
{
    return (n * n) + (n * n * n);
}

// driver code
let n = 4;
document.write(nthTerm(n));

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

Output :

Time complexity: O(1) as only single step is required to calculate nth term from given formula

Auxiliary Space: O(1)

n-th term in series 2, 12, 36, 80, 150....

Explore