Sum of all the numbers in the Nth row of the given triangle

Given a positive integer N, the task is to find the sum of all the numbers in the N^th row of the below triangle. 
 

1 
3 2 
6 2 3 
10 2 3 4 
15 2 3 4 5 
... 
... 
... 
 

Examples: 
 

Input: N = 2 
Output: 5 
3 + 2 = 5
Input: N = 3 
Output: 11 
6 + 2 + 3 = 11 
 

Approach: Taking a closer look at the pattern, it can be observed that a series will be formed as 1, 5, 11, 19, 29, 41, 55, ... whose N^th term is (N - 1) + N².
Below is the implementation of the above approach: 
 

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the sum
// of the nth row elements of
// the given triangle
int getSum(int n)
{
    return ((n - 1) + pow(n, 2));
}

// Driver code
int main()
{
    int n = 3;

    cout << getSum(n);

    return 0;
}

// Java implementation of the approach
class GFG
{
    
// Function to return the sum
// of the nth row elements of
// the given triangle
static int getSum(int n)
{
    return ((n - 1) + (int)Math.pow(n, 2));
}

// Driver code
public static void main(String[] args)
{
    int n = 3;

    System.out.println(getSum(n));
}
}

// This code is contributed by Code_Mech

# Python3 implementation of the approach 

# Function to return the sum 
# of the nth row elements of 
# the given triangle 
def getSum(n) :

    return ((n - 1) + pow(n, 2)); 

# Driver code 
if __name__ == "__main__" : 

    n = 3; 

    print(getSum(n)); 

# This code is contributed by AnkitRai01

// C# implementation of the approach 
using System;
    
class GFG
{
    
// Function to return the sum
// of the nth row elements of
// the given triangle
static int getSum(int n)
{
    return ((n - 1) + (int)Math.Pow(n, 2));
}

// Driver code
public static void Main(String[] args)
{
    int n = 3;

    Console.WriteLine(getSum(n));
}
}

// This code is contributed by 29AjayKumar

<script>

// Javascript implementation of the approach

// Function to return the sum
// of the nth row elements of
// the given triangle
function getSum(n)
{
    return ((n - 1) + Math.pow(n, 2));
}

// Driver code
var n = 3;
document.write(getSum(n));

</script>

11

Time complexity: O(1) because constant operations are done

Auxiliary Space: O(1)

Example-2 in python:

Approach steps:

1.Define a function triangle_row_sum that takes an integer n as input. The function will return the sum of all the numbers in the nth row of a given triangle.
2.Calculate the sum of the nth row of the triangle by using the formula row_sum = 2 * (3^(n-1)). This formula is derived from the fact that the kth row of the triangle has 2 * 3^(k-1) numbers, and each number in the kth row is 3^(k-1) times the corresponding number in the 1st row.
3.Return the value of row_sum as the sum of all the numbers in the nth row of the triangle.
4.In the example usage, create an integer n and call the triangle_row_sum function with this argument. Finally, print the sum of all the numbers in the nth row of the triangle.

#include <iostream>
#include <cmath>

using namespace std;

// function to calculate the sum of the nth row of the triangle
int triangleRowSum(int n) {
    // calculate the sum of the nth row of the triangle
    int rowSum = 2 * pow(3, n - 1);
    // return the sum of the nth row
    return rowSum;
}

// example usage
int main() {
    int n = 4;
    int rowSum = triangleRowSum(n);
    cout << "Sum of all the numbers in the " << n << "th row of the triangle is " << rowSum << endl;
    return 0;
}

// Java program to find the sum of all the numbers in the
// Nth row of a triangle

public class TriangleRowSum {
    public static int triangleRowSum(int n)
    {
        // calculate the sum of the nth row of the triangle
        int rowSum = 2 * (int)Math.pow(3, n - 1);
        // return the sum of the nth row
        return rowSum;
    }

    // example usage
    public static void main(String[] args)
    {
        int n = 4;
        int rowSum = triangleRowSum(n);
        System.out.println(
            "Sum of all the numbers in the " + n
            + "th row of the triangle is " + rowSum);
    }
}

# program to find the sum of all the numbers in the Nth row of a triangle

def triangle_row_sum(n):
    # calculate the sum of the nth row of the triangle
    row_sum = 2 * (3 ** (n-1))
    
    # return the sum of the nth row
    return row_sum

# example usage
n = 4
row_sum = triangle_row_sum(n)
print("Sum of all the numbers in the", n, "th row of the triangle is", row_sum)

// C# program to find the sum of all the numbers in the
// Nth row of a triangle
using System;

public class TriangleRowSum {
  public static int triangleRowSum(int n)
  {

    // calculate the sum of the nth row of the triangle
    int rowSum = 2 * (int)Math.Pow(3, n - 1);

    // return the sum of the nth row
    return rowSum;
  }

  // example usage
  public static void Main(string[] args)
  {
    int n = 4;
    int rowSum = triangleRowSum(n);
    Console.WriteLine(
      "Sum of all the numbers in the " + n
      + "th row of the triangle is " + rowSum);
  }
}

function triangle_row_sum(n)
{

  // calculate the sum of the nth row of the triangle
  const row_sum = 2 * (3 ** (n-1));
  
  // return the sum of the nth row
  return row_sum;
}

// example usage
const n = 4;
const row_sum = triangle_row_sum(n);
console.log(`Sum of all the numbers in the ${n}th row of the triangle is ${row_sum}`);

Sum of all the numbers in the 4 th row of the triangle is 54

Time complexity: O(1)

Auxiliary Space: O(1).