Given a number N, the task is to find the Nth term of this series:
3, 7, 13, 21, 31, …….
Examples:
Input: N = 4
Output: 21
Explanation:
Nth term = (pow(N, 2) + N + 1)
= (pow(4, 2) + 4 + 1)
= 21
Input: N = 11
Output: 133
Approach:
Subtracting these two equations we get
Therefore, the Nth Term of the given series is:
Below is the implementation of the above approach:
C++
// CPP program to find the Nth term of given series. #include <iostream> #include <math.h> using namespace std;
// Function to calculate sum long long int getNthTerm( long long int N)
{ // Return Nth term
return ( pow (N, 2) + N + 1);
} // driver code int main()
{ // declaration of number of terms
long long int N = 11;
// Get the Nth term
cout << getNthTerm(N);
return 0;
} |
Java
// Java code to find the Nth term of given series. import java.util.*;
class solution
{ // Function to calculate sum static long getNthTerm( long N)
{ // Return Nth term
return (( int )Math.pow(N, 2 ) + N + 1 );
} //Driver program public static void main(String arr[])
{ // declaration of number of terms
long N = 11 ;
// Get the Nth term
System.out.println(getNthTerm(N));
} } //THis code is contributed by //Surendra_Gangwar |
Python3
# Python3 Code to find the # Nth term of given series. # Function to calculate sum def getNthTerm(N):
# Return Nth term
return ( pow (N, 2 ) + N + 1 )
# driver code if __name__ = = '__main__' :
# declaration of number of terms N = 11
# Get the Nth term print (getNthTerm(N))
# This code is contributed by # Sanjit_Prasad |
C#
// C# code to find the Nth // term of given series. using System;
class GFG
{ // Function to calculate sum static long getNthTerm( long N)
{ // Return Nth term return (( int )Math.Pow(N, 2) + N + 1);
} // Driver Code static public void Main ()
{ // declaration of number
// of terms
long N = 11;
// Get the Nth term
Console.Write(getNthTerm(N));
} } // This code is contributed by Raj |
Javascript
<script> // JavaScript program to find the Nth term of given series. // Function to calculate sum function getNthTerm(N)
{ // Return Nth term
return (Math.pow(N, 2) + N + 1);
} // driver code // declaration of number of terms
let N = 11;
// Get the Nth term
document.write(getNthTerm(N));
// This code is contributed by Surbhi Tyagi </script> |
PHP
<?php // PHP program to find the // Nth term of given series // Function to calculate sum function getNthTerm( $N )
{ // Return Nth term
return (pow( $N , 2) + $N + 1);
} // Driver code // declaration of number of terms $N = 11;
// Get the Nth term echo getNthTerm( $N );
// This code is contributed by Raj ?> |
Output
133
Time Complexity: O(1)
Space Complexity: O(1) since using constant variables
Method 2: We can also solve the problem by the formula [ (n+1)2-n ].
C++
// CPP program to find the Nth term of given series. #include <iostream> #include <math.h> using namespace std;
// Function to calculate sum long long int getNthTerm( long long int N)
{ // Return Nth term
return ( pow (N + 1, 2) - N);
} // driver code int main()
{ // declaration of number of terms
long long int N = 11;
// Get the Nth term
cout << getNthTerm(N);
return 0;
} |
Java
// Nikunj Sonigara public class Main {
static long getNthTerm( long N) {
return ( long ) (Math.pow(N + 1 , 2 ) - N);
}
public static void main(String[] args) {
long N = 11 ;
System.out.println(getNthTerm(N));
}
} |
Python3
# Python program to find the Nth term of given series. import math
# Function to calculate sum def getNthTerm(N):
# Return Nth term
return int (math. pow (N + 1 , 2 ) - N)
# driver code if __name__ = = '__main__' :
# declaration of number of terms
N = 11
# Get the Nth term
print (getNthTerm(N))
|
C#
using System;
class Program {
// Function to calculate the Nth term of the series
static long GetNthTerm( long N)
{
// Return Nth term
return ( long )(Math.Pow(N + 1, 2) - N);
}
static void Main()
{
// Declaration of the number of terms
long N = 11;
// Get the Nth term
Console.WriteLine(GetNthTerm(N));
}
} |
Javascript
// Nikunj Sonigara function getNthTerm(N) {
return Math.pow(N + 1, 2) - N;
} const N = 11; console.log(getNthTerm(N)); |
Output
133
Time Complexity: O(logN)
Space Complexity: O(1) since using constant variables