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 Nth 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: 2Input: 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 seriesvoid findNthTerm(int n){ cout << n * (3 * n + 1) / 2 << endl;}// Driver codeint main(){ int N = 4; findNthTerm(N); return 0;} |
Java
// Java implementation to// find N-th term in the seriesclass GFG{// Function to find N-th term// in the seriesstatic void findNthTerm(int n){ System.out.print(n * (3 * n + 1) / 2 + "\n");}// Driver codepublic 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 seriesdef findNthTerm(n): print(n * (3 * n + 1) // 2, end = " ");# Driver codeN = 4;findNthTerm(N);# This code is contributed by Code_Mech |
C#
// C# implementation to// find N-th term in the seriesusing System;class GFG{// Function to find N-th term// in the seriesstatic void findNthTerm(int n){ Console.Write(n * (3 * n + 1) / 2 + "\n");}// Driver codepublic 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 seriesfunction findNthTerm(n){ document.write(n * (3 * n + 1) / 2);}// Driver codeN = 4;findNthTerm(N);</script> |
26
Time Complexity: O(1)
Auxiliary space: O(1)
Reference: https://oeis.org/A005449
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