Second Pentagonal numbers

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The second pentagonal numbers are a collection of objects which can be arranged in the form of a regular pentagon.
Second Pentagonal series is:

2, 7, 15, 26, 40, 57, 77, 100, 126, …..

Find the N^th term of the Second Pentagonal Series

Given an integer N. The task is to find the N-th term of the second pentagonal series.

Examples:

Input: N = 1
Output: 2

Input: N = 4
Output: 26

Approach: The idea is to find the general term of the series which can be computed with the help of the following observations as below:

Series = 2, 7, 15, 26, 40, 57, 77, 100, 126, …..
Difference = 7 – 2, 15 – 7, 26 – 15, 40 – 26, …………….
= 5, 8, 11, 14……which is an AP
So nth term of given series
nth term = 2 + (5 + 8 + 11 + 14 …… (n-1)terms)
= 2 + (n-1)/2*(2*5+(n-1-1)*3)
= 2 + (n-1)/2*(10+3n-6)
= 2 + (n-1)*(3n+4)/2
= n*(3*n + 1)/2

Therefore, the Nth term of the series is given as

Below is the implementation of the above approach:

C++

// C++ implementation 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 * (3 * n + 1) / 2
         << endl;
}
 
// Driver code
int main()
{
    int N = 4;
    findNthTerm(N);
 
    return 0;
}

Java

// Java implementation 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.print(n * (3 * 
                     n + 1) / 2 + "\n");
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation to
# find N-th term in the series
 
# Function to find N-th term
# in the series
def findNthTerm(n):
 
    print(n * (3 * n + 1) // 2, end = " ");
 
# Driver code
N = 4;
findNthTerm(N);
 
# This code is contributed by Code_Mech

C#

// C# implementation 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 * (3 * 
                  n + 1) / 2 + "\n");
}
 
// Driver code
public static void Main()
{
    int N = 4;
    findNthTerm(N);
}
}
 
// This code is contributed by Code_Mech

Javascript

<script>
 
// Javascript implementation t
// find N-th term in the series
 
// Function to find N-th term
// in the series
function findNthTerm(n)
{
    document.write(n * (3 * n + 1) / 2);
}
 
// Driver code
N = 4;
findNthTerm(N);
 
</script>

Output:

Time Complexity: O(1)
Auxiliary space: O(1)

Reference: https://oeis.org/A005449

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