Program to find the Nth number of the series 2, 10, 24, 44, 70…..

Given a number N, the task is to find the Nth (N may be up to 10^18) term of this series: 

2, 10, 24, 44, 70….. 

The answer can be very large so print answer under modulo 10^9+9.

Examples:

Input: N = 2
Output: 10

Input: N = 5
Output: 70

Approach:The formula for Nth term will be:  

Nth term = 3*n*n – n 

Below is the implementation of the above approach: 

C++

// CPP program to find
// the Nth term of the series
// 2, 10, 24, 44, 70.....

#include <bits/stdc++.h>
using namespace std;

#define mod 1000000009

// function to return nth term of the series
int NthTerm(long long n)
{
    long long x = (3 * n * n) % mod;
    return (x - n + mod) % mod;
}

// Driver code
int main()
{

// Get N
    long long N = 4;

    // Get Nth term
    cout << NthTerm(N);

    return 0;
}

C

// C program to find
// the Nth term of the series
// 2, 10, 24, 44, 70.....
#include <stdio.h>

#define mod 1000000009

// function to return nth term of the series
int NthTerm(long long n)
{
    long long x = (3 * n * n) % mod;
    return (x - n + mod) % mod;
}

// Driver code
int main()
{

// Get N
    long long N = 4;

    // Get Nth term
    printf("%d",NthTerm(N));

    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java program to find N-th
// term of the series:

import java.util.*;
import java.lang.*;
import java.io.*;

class GFG {

    // function to return nth term of the series
    static long NthTerm(long n)
    {
        long x = (3 * n * n) % 1000000009;
        return (x - n + 1000000009) % 1000000009;
    }

    // Driver Code
    public static void main(String args[])
    {

        // Taking  n as 4
        long N = 4;

        // Printing the nth term
        System.out.println(NthTerm(N));
    }
}

Python3

# Python 3 program to find
# N-th term of the series:


# Function for calculating
# Nth term of series
def NthTerm(N) :

    # return nth term
    x = (3 * N*N)% 1000000009
    return ((x - N + 1000000009)% 1000000009)

# Driver code
if __name__ == "__main__" :

    N = 4

    # Function Calling
    print(NthTerm(N))

C#

// C# program to find N-th
// term of the series:
using System;
class GFG
{

// function to return nth
// term of the series
static long NthTerm(long n)
{
    long x = (3 * n * n) % 1000000009;
    return (x - n + 1000000009) % 1000000009;
}

// Driver Code
public static void Main()
{

    // Taking n as 4
    long N = 4;

    // Printing the nth term
    Console.Write(NthTerm(N));
}
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP program to find
// the Nth term of the series
// 2, 10, 24, 44, 70.....

// function to return Nth
// term of the series
function NthTerm($n)
{
    $mod = 1000000009;

    $x = (3 * $n * $n) % $mod;
    return ($x - $n + $mod) % $mod;
}

// Driver code
$N = 4;

// Get Nth term
echo NthTerm($N);

// This code is contributed
// by Mahadev99
?>

Javascript

<script>

// Javascript program to find N-th
// term of the series:

    // function to return nth term of the series
    function NthTerm( n) {
        let x = (3 * n * n) % 1000000009;
        return (x - n + 1000000009) % 1000000009;
    }

    // Driver Code


        // Taking n as 4
        let N = 4;

        // Printing the nth term
        document.write(NthTerm(N));

// This code contributed by Princi Singh

</script>

Output:

44

Time Complexity: O(1)

Auxiliary Space: O(1)