Find nth term of the series 5 2 13 41
Given a number N, the task is to find the nth term of the series
5, 2, 19, 13, 41, 31, 71, 57….
It is given that value of n can range between 1 and 10000.
Examples:
Input: N = 4
Output:13Input: N = 15
Output:272
Approach: The problem looks very hard but approach is very simple. If the value of n is given as an odd number, the nth term will be ( ( n + 1 ) ^ 2 ) + n.
Otherwise, it will be ( ( n – 1 ) ^ 2 ) + n.
Implementation:
C++
// C++ program to find nth term of // the series 5 2 13 41 #include<bits/stdc++.h> using namespace std; // function to calculate nth term of the series int nthTermOfTheSeries( int n) { // to store the nth term of series int nthTerm; // if n is even number if (n % 2 == 0) nthTerm = pow (n - 1, 2) + n; // if n is odd number else nthTerm = pow (n + 1, 2) + n; // return nth term return nthTerm; } // Driver code int main() { int n; n = 8; cout << nthTermOfTheSeries(n) << endl; n = 12; cout << nthTermOfTheSeries(n) << endl; n = 102; cout << nthTermOfTheSeries(n) << endl; n = 999; cout << nthTermOfTheSeries(n) << endl; n = 9999; cout << nthTermOfTheSeries(n) << endl; return 0; } // This code is contributed // by Akanksha Rai |
C
// C program to find nth term of // the series 5 2 13 41 #include <math.h> #include <stdio.h> // function to calculate nth term of the series int nthTermOfTheSeries( int n) { // to store the nth term of series int nthTerm; // if n is even number if (n % 2 == 0) nthTerm = pow (n - 1, 2) + n; // if n is odd number else nthTerm = pow (n + 1, 2) + n; // return nth term return nthTerm; } // Driver code int main() { int n; n = 8; printf ( "%d\n" , nthTermOfTheSeries(n)); n = 12; printf ( "%d\n" , nthTermOfTheSeries(n)); n = 102; printf ( "%d\n" , nthTermOfTheSeries(n)); n = 999; printf ( "%d\n" , nthTermOfTheSeries(n)); n = 9999; printf ( "%d\n" , nthTermOfTheSeries(n)); return 0; } |
Java
// Java program to find nth term of the series 5 2 13 41 import java.lang.Math; class GFG { // function to calculate nth term of the series static long nthTermOfTheSeries( int n) { // to store the nth term of series long nthTerm; // if n is even number if (n % 2 == 0 ) nthTerm = ( long )Math.pow(n - 1 , 2 ) + n; // if n is odd number else nthTerm = ( long )Math.pow(n + 1 , 2 ) + n; // return nth term return nthTerm; } // Driver code public static void main(String[] args) { int n; n = 8 ; System.out.println( nthTermOfTheSeries(n)); n = 12 ; System.out.println( nthTermOfTheSeries(n)); n = 102 ; System.out.println( nthTermOfTheSeries(n)); n = 999 ; System.out.println( nthTermOfTheSeries(n)); n = 9999 ; System.out.println( nthTermOfTheSeries(n)); //This code is contributed by 29AjayKumar } } |
Python3
# Python3 program to find nth term # of the series 5 2 13 41 from math import pow # function to calculate nth term # of the series def nthTermOfTheSeries(n): # to store the nth term of series # if n is even number if (n % 2 = = 0 ): nthTerm = pow (n - 1 , 2 ) + n # if n is odd number else : nthTerm = pow (n + 1 , 2 ) + n # return nth term return nthTerm # Driver code if __name__ = = '__main__' : n = 8 print ( int (nthTermOfTheSeries(n))) n = 12 print ( int (nthTermOfTheSeries(n))) n = 102 print ( int (nthTermOfTheSeries(n))) n = 999 print ( int (nthTermOfTheSeries(n))) n = 9999 print ( int (nthTermOfTheSeries(n))) # This code is contributed by # Shashank_Sharma |
C#
// C# program to find nth term // of the series 5 2 13 41 using System; class GFG { // function to calculate // nth term of the series static long nthTermOfTheSeries( int n) { // to store the nth term of series long nthTerm; // if n is even number if (n % 2 == 0) nthTerm = ( long )Math.Pow(n - 1, 2) + n; // if n is odd number else nthTerm = ( long )Math.Pow(n + 1, 2) + n; // return nth term return nthTerm; } // Driver code public static void Main() { int n; n = 8; Console.WriteLine(nthTermOfTheSeries(n)); n = 12; Console.WriteLine( nthTermOfTheSeries(n)); n = 102; Console.WriteLine( nthTermOfTheSeries(n)); n = 999; Console.WriteLine( nthTermOfTheSeries(n)); n = 9999; Console.WriteLine( nthTermOfTheSeries(n)); } } // This code is contributed by Ryuga |
PHP
<?php // Php program to find nth term of // the series 5 2 13 41 // function to calculate nth term // of the series function nthTermOfTheSeries( $n ) { // if n is even number if ( $n % 2 == 0) $nthTerm = pow( $n - 1, 2) + $n ; // if n is odd number else $nthTerm = pow( $n + 1, 2) + $n ; // return nth term return $nthTerm ; } // Driver code $n = 8; echo nthTermOfTheSeries( $n ) . "\n" ; $n = 12; echo nthTermOfTheSeries( $n ) . "\n" ; $n = 102; echo nthTermOfTheSeries( $n ) . "\n" ; $n = 999; echo nthTermOfTheSeries( $n ) . "\n" ; $n = 9999; echo nthTermOfTheSeries( $n ) . "\n" ; // This code is contributed by ita_c ?> |
Javascript
<script> // Javascript program to find nth term of // the series 5 2 13 41 // function to calculate nth term of the series function nthTermOfTheSeries(n) { // to store the nth term of series let nthTerm; // if n is even number if (n % 2 == 0) nthTerm = Math.pow(n - 1, 2) + n; // if n is odd number else nthTerm = Math.pow(n + 1, 2) + n; // return nth term return nthTerm; } // Driver code let n; n = 8; document.write(nthTermOfTheSeries(n) + "<br>" ); n = 12; document.write(nthTermOfTheSeries(n) + "<br>" ); n = 102; document.write(nthTermOfTheSeries(n) + "<br>" ); n = 999; document.write(nthTermOfTheSeries(n) + "<br>" ); n = 9999; document.write(nthTermOfTheSeries(n) + "<br>" ); // This code is contributed by rishavmahato348. </script> |
Output:
57 133 10303 1000999 100009999
Time Complexity: O(1) as it is doing constant operations
Auxiliary Space: O(1) since no extra array is used space taken by this algorithm is constant
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