# Second heptagonal numbers

The Second heptagonal numbers series can be represented as

4, 13, 27, 46, 70, 99, 133, 172, 216, …..

Nth term

Given an integer N. The task is to find the N-th term of the given series.
Examples:

Input: N = 1
Output: 4

Input: N = 4
Output: 46

Approach: The idea is to find the general term for the Second heptagonal numbers. Below is the computation of the general term for second heptagonal numbers:

Series = 4, 13, 27, 46, 70, 99, 133, 172, 216, …..
Difference = 13-4, 27-13, 46-27, 70-46, …………….
Difference = 9, 14, 19, 24……which is a AP
So nth term of given series
nth term = 4 + (9 + 14 + 19 + 24 …… (n-1)terms)
nth term = 4 + (n-1)/2*(2*9+(n-1-1)*5)
nth term = 4 + (n-1)/2*(18+5n-10)
nth term = 4 + (n-1)*(5n+8)/2
nth term = n*(5*n+3)/2
Therefore, the Nth term of the series is given as

Below is the implementation of above approach:

## C++

 // C++ implementation to// find N-th term in the series #include #include using namespace std; // Function to find N-th term// in the seriesvoid findNthTerm(int n){    cout << n * (5 * n + 3) / 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 series static void findNthTerm(int n) {     System.out.println(n * (5 * n + 3) / 2); }  // Driver code public static void main(String[] args) {     int N = 4;          findNthTerm(N); } }  // This code is contributed by Ritik Bansal

## Python 3

 # Python implementation to # find N-th term in the series  # Function to find N-th term # in the series def findNthTerm(n):    print(n * (5 * n + 3) // 2)  # Driver codeN = 4 # Function callfindNthTerm(N)  # This code is contributed by Vishal Maurya.

## C#

 // C# implementation to// find N-th term in the seriesusing System;class GFG{  // Function to find N-th term // in the series static void findNthTerm(int n) {     Console.Write(n * (5 * n + 3) / 2); }  // Driver code public static void Main() {     int N = 4;          findNthTerm(N); } }  // This code is contributed by Code_Mech

## Javascript

 

Output:
46

Time Complexity: O(1)

Auxiliary Space: O(1)

Reference:OEIS

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