Calculating and Displaying the Sum of Multiples of 3 and 5 from 1 to 100: A Comprehensive Guide

This guide aims to explain how to calculate and display the sum of all multiples of 3 and 5 within the range of 1 to 100, using both pseudocode and Python programming. We will also provide a deeper understanding of the logic behind the implementation and explore various versions of the pseudocode to achieve the desired result.

Purpose and Significance

The problem of calculating the sum of multiples of 3 and 5, often referred to as the 3 and 5 sum problem, is a common programming challenge seen in various contexts. This problem not only helps in understanding fundamental programming techniques like loops and conditional statements but also serves as a stepping stone to more complex programming concepts.

Understanding the Problem

To find the sum of all multiples of 3 and 5 from 1 to 100, the following steps can be followed:

Initialize a variable to hold the sum, for instance, sum 0. Loop through the numbers from 1 to 100. For each number, check if it is a multiple of 3 or 5. If it is, add it to the sum. After the loop, display the sum.

Here is the pseudocode representation of the program:

STARTSET sum  0FOR number FROM 1 TO 100 DOIF number MOD 3  0 OR number MOD 5  0 THENsum  sum   numberEND IFEND FORDISPLAY sumEND

Pseudocode Explanation

SET sum 0: Initializes the sum variable to zero. FOR number FROM 1 TO 100 DO: Loops through each number from 1 to 100. IF number MOD 3 0 OR number MOD 5 0 THEN: Checks if the current number is divisible by 3 or 5. sum sum number: Adds the number to the sum if the condition is met. DISPLAY sum: Outputs the final sum after completing the loop.

Python Implementation Example

A simple Python implementation to demonstrate the logic would be:

sum  0for number in range(1, 101):    if number % 3  0 or number % 5  0:        sum  sum   numberprint(sum)

When you run this code, it will calculate and display the sum of all multiples of 3 and 5 from 1 to 100, which is 2418.

Versions of Pseudocode

The below pseudocode versions were derived based on the book "Simple Program Design" by Lesley Anne Robertson. These versions illustrate different ways of approaching the problem:

Version 1

Sum_3_5_MultiplesSet i to zeroSet sum to zeroFOR i  1 to 101 i  i   1 DO  IF i mod 3  0 THEN    Print iELSE    IF i mod 5  0 THEN        Print i    ELSE        sum  sum   i        Print i    END IFEND IFEND FORPrint sum

Version 2

Sum_3_5_MultiplesSet i to zeroSet sum to zeroFOR i  1 to 101 i  i   1 DO  IF i mod 3  0 AND i mod 5  0 THEN    sum  sum   i    Print iEND IFEND FORPrint sum

Version 3

Sum_3_5_MultiplesSet i to zeroSet sum to zeroFOR i  0 to 101 i  i   15 DO  sum  sum   iPrint iEND FORPrint sum

Version 4

Sum_3_5_MultiplesSet i to zeroSet sum to zeroFOR i  1 to 101 i  i   1 DO  IF i mod 15  0 THEN    Print iELSE    sum  sum   iEND IFEND FORPrint sum

Conclusion

The problem of finding the sum of multiples of 3 and 5 from 1 to 100 is a great way to practice fundamental programming skills. Whether you use pseudocode or a specific programming language, understanding the logic and implementing the solution can significantly enhance your problem-solving capabilities. For further reading and understanding, consider checking out the book "Simple Program Design" by Lesley Anne Robertson.

Related Topics and Resources

Keyword 1: sum of multiples Learn more about calculating the sum of multiples of different numbers and how it can be applied in real-world scenarios. Keyword 2: programming pseudocode Explore the basics of pseudocode, a form of detailed outline or structured documentation that represents the control flow of a program. Keyword 3: Python implementation Get a hands-on guide on implementing programming solutions using the Python language.