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Program to find the Nth number of the series 2, 10, 24, 44, 70…..
  • Last Updated : 24 Mar, 2021

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;
}

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;
 
        // Prleting the nth term
        document.write(NthTerm(N));
 
// This code contributed by Princi Singh
 
</script>
Output: 
44

 

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