Given a series 9, 33, 73, 129… Find the n-th term of the series.
Examples:
Input : n = 4
Output : 129Input : 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++
// 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
201
Time Complexity: O(1), as we are using not using any loop or recursion to traverse.
Auxiliary Space: O(1), as we are not using any extra space.