Given a number N, the task is to write a program to find the N-th term of the Central polygonal numbers series:
1, 1, 3, 7, 13, 21, 31, 43, 57…..
Examples:
Input: N = 0 Output: 1 Input: N = 3 Output: 7
Approach: The Nth term can be formalized as:
Series = 1, 3, 7, 13, 21, 31, 43, 57……
Difference = 3-1, 7-3, 13-7, 21-13…………….
Difference = 2, 4, 6, 8……which is a AP
So nth term of given series
= 1 + (2, 4, 6, 8 …… (n-1)terms)
= 1 + (n-1)/2*(2*2+(n-1-1)*2)
= 1 + (n-1)/2*(4+2n-4)
= 1 + (n-1)*n
= n^2 – n + 1
Therefore, the Nth term of the series is given as
Below is the implementation of above approach:
C++
// C++ program to find N-th term // in the series #include <iostream> #include <math.h> using namespace std;
// Function to find N-th term // in the series void findNthTerm( int n)
{ cout << n * n - n + 1 << endl;
} // Driver code int main()
{ int N = 4;
findNthTerm(N);
return 0;
} |
Java
// Java program to find N-th term // in the series class GFG{
// Function to find N-th term // in the series static void findNthTerm( int n)
{ System.out.println(n * n - n + 1 );
} // Driver code public static void main(String[] args)
{ int N = 4 ;
findNthTerm(N);
} } // This code is contributed by Ritik Bansal |
Python3
# Python3 program to find N-th term # in the series # Function to find N-th term # in the series def findNthTerm(n):
print (n * n - n + 1 )
# Driver code N = 4
# Function Call findNthTerm(N) # This code is contributed by Vishal Maurya |
C#
// C# program to find N-th term // in the series using System;
class GFG{
// Function to find N-th term // in the series static void findNthTerm( int n)
{ Console.Write(n * n - n + 1);
} // Driver code public static void Main()
{ int N = 4;
findNthTerm(N);
} } // This code is contributed by nidhi_biet |
Javascript
<script> // Javascript program to find N-th term // in the series // Function to find N-th term // in the series function findNthTerm(n)
{ document.write(n * n - n + 1);
} // Driver code N = 4; findNthTerm(N); </script> |
Output:
13
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