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)

This article is contributed by Striver. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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

Recommended Posts: