Question

Threes: Make a list of the multiples of 3 from 3 to 30. Use a for loop to print the numbers in your list.

Short answer

The multiples of 3 from 3 to 30 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30.

Step-by-step solution

Understand the Problem

We are tasked with creating a list of multiples of 3 starting from 3 up to 30, and then using a programming construct (a loop) to print out these values.

Identify the Range

The multiples of 3 we need to find start at 3 and end at 30. This translates to finding the set: 3, 6, 9, ..., up to 30.

Construct the Multiples of 3 List

To get all multiples of 3 from 3 to 30, consider multiples like this: Starting number is 3 and keep adding 3 each time until you reach 30.

Use a For Loop

We will use a for loop to iterate over a range from 3 to 30. In each iteration, we will print the current number if it is divisible by 3. In Python, this can be done using a loop: ```python for number in range(3, 31): if number % 3 == 0: print(number) ```

Verify and Print Solution

Run the for loop code, and ensure each printed number is a multiple of 3 and lies within the given range. Confirm that the output is the numbers: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. This verifies the solution is correct.

Key concepts

Understanding For Loops in Python

For loops in Python are a way to iterate over a sequence (such as a list, tuple, dictionary, set, or even a string) and execute a block of code multiple times. In the context of the problem we're solving, for loops help us traverse numbers from a starting point to an ending point with a specified increment. This allows us to go over each number in a range, evaluating whether it meets certain conditions or performing actions based upon it.

For example, when we write `for number in range(3, 31):`, the loop variable `number` takes on each subsequent value in the specified range, executing the code block inside the loop for each value. This kind of structured repetition simplifies tasks that involve processing sequential elements and is particularly useful in tasks like list creation or data processing.

Using for loops effectively prevents repeated code and makes our codebase cleaner and easier to manage.

Exploring the Range Function

The range function in Python is a powerful tool that generates a sequence of numbers starting from the given start value up to, but not including, the end value. It can take up to three arguments: `start`, `stop`, and `step`. When used in the context of a for loop, it allows us to specify the exact sequence of numbers over which the loop should iterate.

In this exercise, we used `range(3, 31)`, which generates numbers from 3 to 30. The default step value is 1; however, a custom step can be specified by providing a third argument. If we needed every other number, `range(3, 31, 2)` would work.

The range function is quite useful for creating loops within specific numerical limits, especially when creating lists of numbers or iterating over such lists.

Using the Modulus Operator

The modulus operator `%` in Python is used to determine the remainder of division of one number by another. In the context of our problem, we used the modulus operator to check if a number is a multiple of another number, particularly to check for multiples of 3.

By writing `if number % 3 == 0:`, we are effectively saying, "Check if dividing this number by 3 leaves a remainder of 0." If this condition is true, the number is a multiple of 3, hence getting printed in our loop.

This operator is quite useful for checking divisibility, determining even or odd numbers, and much more. Understanding the modulus operator is essential for various programming tasks, where conditions based upon divisibility are needed.

List Creation in Python

Lists are a fundamental data structure in Python that allow you to collect and organize data. They can hold an ordered collection of items, which are changeable and allow duplicate entries.

To create a list in Python, you enclose your items within square brackets `[ ]`. For instance, `multiples_of_three = [3, 6, 9, ...]` creates a list of multiples of 3. You can also build lists programmatically using loops and other functions.

In our exercise, you could also use a comprehension to generate the list of multiples of 3: `multiples_of_three = [x for x in range(3, 31) if x % 3 == 0]`. This technique is known as list comprehension and is a very concise way to create lists while applying specific conditions.

Lists in Python provide numerous methods and allow for efficient manipulations, making them an indispensable tool in many programming endeavors.