Find Nth term of the series 0, 2, 4, 8, 12, 18…

Given a number N. The task is to write a program to find the Nth term in the below series:

0, 2, 4, 8, 12, 18…

Examples:

Input: 3
Output: 4
For N = 3
Nth term = ( 3 + ( 3 - 1 ) * 3 ) / 2
         = 4
Input: 5 
Output: 12

On observing carefully, the Nth term in the above series can be generalized as:

Nth term = ( N + ( N - 1 ) * N ) / 2

Below is the implementation of the above approach:



C++

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// CPP program to find N-th term of the series:
// 0, 2, 4, 8, 12, 18...
#include <iostream>
using namespace std;
  
// Calculate Nth term of series
int nthTerm(int N)
{
    return (N + N * (N - 1)) / 2;
}
  
// Driver Function
int main()
{
    int N = 5;
  
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to find N-th term of the series:
// 0, 2, 4, 8, 12, 18...
import java.io.*;
  
// Main class for main method
class GFG {
    public static int nthTerm(int N)
    {
        // By using above formula
        return (N + (N - 1) * N) / 2;
    }   
   
    // Driver code
    public static void main(String[] args)
    {
        int N = 5; // 5th term is 12
              
        System.out.println(nthTerm(N));
    }
}

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Python 3

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# Python 3 program to find N-th term of the series: 
# 0, 2, 4, 8, 12, 18.
  
# Calculate Nth term of series
def nthTerm(N) :
      
    return (N + N * (N - 1)) // 2
  
# Driver Code
if __name__ == "__main__" :
  
    N = 5
  
    print(nthTerm(N))
  
# This code is contributed by ANKITRAI1

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C#

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// C# program to find N-th term of the series:
// 0, 2, 4, 8, 12, 18...
using System;
class gfg
{   
    // Calculate Nth term of series
    public int nthTerm(int N)
    {
        int n = ((N + N * (N - 1)) / 2);
        return n;
    }
  
    //Driver program
    static void Main(string[] args)
    {
        gfg p = new gfg();
        int a = p.nthTerm(5);
        Console.WriteLine(a);
        Console.Read();
    }
}
//This code is contributed by SoumikMondal

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PHP

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<?php
// PHP program to find 
// N-th term of the series:
// 0, 2, 4, 8, 12, 18...
  
// Calculate Nth term of series
function nthTerm($N)
{
    return (int)(($N + $N *
                 ($N - 1)) / 2);
}
  
// Driver Code
$N = 5;
  
echo nthTerm($N);
  
// This code is contributed by mits
?>

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Output:

12

Time Complexity: O(1)

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