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> |
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.
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