Find n-th term in the series 9, 33, 73,129 …

Given a series 9, 33, 73, 129… Find the n-th term of the series.

Examples:

Input : n = 4
Output : 129 

Input : n = 5
Output : 201

The given series has a pattern which is visible after subtracting it from itself after one shift 

S = 9 + 33 + 73 + 129 + … tn-1 + tn
S =     9 + 33 + 73 + … tn-2 + tn-1 + tn
———————————————
0 = 9 + (24 + 40 + 56 + ….) - tn 

Since 24 + 40 + 56.. series in A.P with
common difference of 16, we get

 tn = 9 + [((n-1)/2)*(2*24 + (n-1-1)d)] 

On solving this we get 



 tn = 8n2 + 1

Below is the implementation of the above approach:

C++

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// Program to find n-th element in the
// series 9, 33, 73, 128..
#include <bits/stdc++.h>
using namespace std;
  
// Returns n-th  element of the series
int series(int n)
{
    return (8 * n * n) + 1;
}
  
// driver program to test the above function
int main()
{
    int n = 5;
    cout << series(n);
    return 0;
}

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Java














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// Program to find n-th element in the 


// series 9, 33, 73, 128.. 


import java.io.*; 


  


class GFG{ 


      


    // Returns n-th  element of the series 


    static int series(int n) 


    { 


        return (8 * n * n) + 1; 


    } 


      


    // driver program to test the above 


    // function 


    public static void main(String args[]) 


    { 


        int n = 5; 


        System.out.println(series(n)); 


    } 


} 


  


/*This code is contributed by Nikita Tiwari.*/



















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Python3














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# Python Program to find n-th element  


# in the series 9, 33, 73, 128... 


  


# Returns n-th element of the series 


def series(n): 


    print (( 8 * n ** 2) + 1) 


      


# Driver Code 


series(5) 


  


# This code is contributed by Abhishek Agrawal. 



















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C#














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// C# program to find n-th element in the 


// series 9, 33, 73, 128.. 


using System; 


  


class GFG { 


  


    // Returns n-th element of the series 


    static int series(int n) 


    { 


        return (8 * n * n) + 1; 


    } 


  


    // driver function 


    public static void Main() 


    { 


        int n = 5; 


        Console.WriteLine(series(n)); 


    } 


} 


  


/*This code is contributed by vt_m.*/



















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PHP














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<?php 


// PHP Program to find n-th element  


// in the series 9, 33, 73, 128.. 


  


// Returns n-th element 


// of the series 


function series($n) 


{ 


    return (8 * $n * $n) + 1; 


} 


  


// Driver Code 


$n = 5; 


echo(series($n)); 


  


// This code is contributed by Ajit. 


?> 



















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Output:


201



Time complexity: O(1)


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