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

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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

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

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

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

On solving this we get 


 t_n = 8n² + 1

Below is the implementation of the above approach:

C++

// 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; 
} 

Java

// 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.*/

Python3

# 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. 

C#

// 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.*/

PHP

<?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. 
?> 

Output:

Time complexity: O(1)

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My Personal Notes

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

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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