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

Difficulty Level : Easy
Last Updated : 16 Apr, 2021

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

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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 = 8n^{2 + 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.
?>

Javascript

<script>
 
// 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 program to test the above function
let n = 5;
document.write(series(n));
 
</script>

Output:

Time complexity: O(1)
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Find n-th term in the series 9, 33, 73,129 …

C++

Java

Python3

C#

PHP

Javascript