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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Improved By : jit_t



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