findTriangularNumbersRange()

Step 1: Understand what a Triangular Number is

The first step in creating a function to find triangular numbers is understanding what a triangular number is. A triangular number is a number that can form an equilateral triangle. It is the sum of the natural numbers up to a certain point. For example, the first few triangular numbers are 1, 3, 6, 10, 15.

    1
   1 2
  1 2 3
 1 2 3 4
1 2 3 4 5

As shown above, each line represents a triangular number.

Step 2: Setting Up the Program Structure

The next step is to start defining our function which will take two integers start and end as the parameters.

function findTriangularNumbersRange(start, end) {
  // The code will be added here.
}

Step 3: Creating the Loop

We will then create a loop that starts with the start parameter value and ends with the value of the end parameter.

function findTriangularNumbersRange(start, end) {
  for(let i = start; i <= end; i++){
      
  }
}

Step 4: Calculating the Triangular Numbers

In the loop body, we will calculate triangular numbers. The ith triangular number is the sum of the numbers from 1 to i. This sum can be computed by using the formula i * (i + 1) / 2. This formula derives from the sum of an arithmetic series.

function findTriangularNumbersRange(start, end) {
  for(let i = start; i <= end; i++){
      let triangularNumber = i * (i + 1) / 2;
  }
}

Step 5: Store the resulting Triangular Numbers

Lastly, we will store each calculated triangular number in an array.

function findTriangularNumbersRange(start, end) {
  let result = [];
  for(let i = start; i <= end; i++){
      let triangularNumber = i * (i + 1) / 2;
      result.push(triangularNumber);
  }
  return result;
}

Conclusion

The function findTriangularNumbersRange will return an array of triangular numbers within the provided range. The essence of this function is the computation of the triangular number inside a loop that increments up to the end of the range. The computation uses a mathematical formula for the sum of natural numbers, which yields the triangular numbers.