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++

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// 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;
}

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Java

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// 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));
    }
}

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Python3

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# 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)) 

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C#

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// 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

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PHP

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<?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
?>

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Output:

44


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Improved By : Mahadev99, Ita_c