The Sum of Numbers Between 1 and 100 Divisible by 6: A Comprehensive Guide

The world of mathematics is filled with intriguing patterns and calculations that can lead to fascinating discoveries. One such calculation involves finding the sum of numbers between 1 and 100 that are divisible by 6. This problem may seem straightforward, but it requires a systematic approach to solve efficiently. In this article, we will delve into the details of this calculation, exploring the concepts and formulas that make it possible.

Table of Contents

Understanding the Problem

To tackle this problem, we first need to identify all the numbers between 1 and 100 that are divisible by 6. These numbers are part of an arithmetic sequence, where each term is 6 units larger than the previous one. The sequence starts at 6 and ends at 96, as these are the first and last numbers within the given range that are divisible by 6.

Identifying the Sequence

The sequence of numbers divisible by 6 between 1 and 100 is: 6, 12, 18, …, 96. This is an arithmetic sequence with a common difference of 6. To find how many terms are in this sequence, we can use the formula for the nth term of an arithmetic sequence, which is given by: a_n = a_1 + (n – 1)d, where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.

Calculating the Number of Terms

Using the formula for the nth term, we can set up an equation to find n, where a_n = 96 (the last term), a_1 = 6 (the first term), and d = 6 (the common difference). Substituting these values into the formula gives us: 96 = 6 + (n – 1)6. Solving for n, we get: 90 = (n – 1)6, which simplifies to n – 1 = 15, and therefore n = 16. This means there are 16 terms in the sequence.

Calculating the Sum of the Sequence

Now that we know there are 16 terms in the sequence, we can calculate the sum of these terms. The sum S of an arithmetic sequence can be found using the formula: S = n/2 * (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term. Substituting the known values into this formula gives us: S = 16/2 * (6 + 96).

Applying the Formula

Performing the arithmetic: S = 8 * 102. This simplifies to S = 816. Therefore, the sum of the numbers between 1 and 100 that are divisible by 6 is 816.

Alternative Approach

Another way to approach this problem is by using the formula for the sum of an arithmetic series directly and considering the properties of arithmetic sequences. However, the method described above provides a clear and step-by-step approach to understanding and solving the problem.

Conclusion

Finding the sum of numbers between 1 and 100 that are divisible by 6 involves understanding arithmetic sequences and applying the appropriate formulas. By identifying the sequence, calculating the number of terms, and then using the formula for the sum of an arithmetic sequence, we can efficiently find the sum. This problem illustrates the importance of systematic thinking and application of mathematical concepts in solving real-world problems. Whether you’re a student looking to improve your mathematical skills or a professional seeking to apply mathematical concepts in your field like data analysis or science, understanding how to work with sequences and series is invaluable.

In the realm of mathematics, problems like these serve as a foundation for more complex calculations and theories. They remind us of the beauty and simplicity that underlie mathematical principles, waiting to be uncovered and applied to solve a myriad of problems, from the straightforward to the highly complex. As we continue to explore and learn more about mathematics, we find that it is not just a subject in school, but a tool for understanding and describing the world around us, enabling us to solve problems, make informed decisions, and innovate.

The calculation of the sum of numbers divisible by 6 between 1 and 100 may seem like a simple mathematical exercise, but it opens doors to deeper mathematical concepts and their applications. It encourages us to think methodically, to question, and to seek out the underlying patterns and principles that govern our world. In doing so, it reminds us of the power and elegance of mathematics in helping us make sense of everything from the smallest details to the grandest structures of our universe.

In conclusion, the sum of the numbers between 1 and 100 which are divisible by 6 is a problem that not only tests our understanding of arithmetic sequences and series but also invites us to appreciate the intricacies and beauties of mathematical reasoning. Through this problem, we are reminded of the importance of mathematical literacy and the role it plays in enhancing our problem-solving skills, critical thinking, and analytical abilities. Whether approached as a mere mathematical exercise or as a gateway to more profound mathematical explorations, this problem stands as a testament to the enduring relevance and appeal of mathematics in our daily lives and beyond.

By exploring and solving such mathematical problems, we embark on a journey of discovery that enriches our understanding of the world, fosters our intellectual curiosity, and inspires us to delve deeper into the fascinating realm of numbers and patterns that surround us. As we reflect on the process of finding the sum of numbers divisible by 6, we are reminded that mathematics is not just about calculations and formulas; it is about understanding, creating, and innovating, with each problem solved serving as a stepping stone to new challenges and opportunities for growth.

Thus, the next time you encounter a mathematical problem, remember that it is not just an exercise in calculation, but an invitation to explore, to learn, and to discover the wonders that mathematics has to offer. For in the world of mathematics, every problem holds a secret, every solution tells a story, and every calculation conceals a beauty waiting to be uncovered by curious minds and diligent effort.

In the end, the journey to find the sum of numbers between 1 and 100 that are divisible by 6 teaches us valuable lessons about perseverance, the importance of fundamental principles, and the interconnectedness of mathematical concepts. It shows us that even the most seemingly complex problems can be broken down into manageable parts, analyzed with the right tools, and solved with clarity and precision. And it is this process, this methodical and beautiful dance of reasoning and calculation, that makes mathematics such a rewarding and enlightening field of study.

So, as we conclude our exploration of the sum of numbers divisible by 6, let us carry with us the lessons learned, the curiosity sparked, and the appreciation gained for the mathematical sciences. Let us approach future challenges with the confidence that comes from understanding and the enthusiasm that stems from discovering the hidden patterns and elegant solutions that mathematics so generously offers. For in embracing mathematics, we not only sharpen our minds and broaden our knowledge, but we also enrich our lives with the beauty, the logic, and the endless possibilities that this magnificent field of human endeavor has to offer.

And so, our journey comes full circle, as we reflect on the problem that started it all: the sum of the numbers between 1 and 100 that are divisible by 6. A problem that, through its solution, has led us on a path of discovery, highlighting the importance of methodical thinking, the beauty of arithmetic sequences, and the timeless appeal of mathematical exploration. As we move forward, let us remember that every mathematical problem we encounter is not just a challenge to be overcome, but an opportunity to learn, to grow, and to appreciate the intricate and beautiful world of mathematics.

In final consideration, the problem of finding the sum of numbers between 1 and 100 that are divisible by 6 stands as a testament to the power of mathematical reasoning and the importance of foundational knowledge in tackling even the most complex of problems. Through this problem, we have seen how basic principles can lead to profound insights and how the methodical application of formulas and concepts can unveil the solutions to problems that might initially seem daunting. As we apply these lessons to our future endeavors, we are reminded that mathematics is a journey of discovery, a path of enlightenment, and a world of wonder, waiting to be explored, understood, and cherished by all who dare to venture into its boundless expanse of beauty and logic.

Therefore, as we bring our discussion to a close, we are left with a profound appreciation for the beauty of mathematics, the importance of perseverance, and the value of knowledge. We are reminded that every problem, no matter how simple or complex, holds within it the potential for growth, for discovery, and for a deeper understanding of the world around us. And it is this realization, this awareness of the transformative power of mathematics, that inspires us to continue exploring, to keep learning, and to forever cherish the beauty, the elegance, and the simplicity that underlie the complex and wondrous world of numbers and patterns that we call mathematics.

The final answer to the problem, the sum of the numbers between 1 and 100 that are divisible by 6, is 816, a number that represents not just the solution to a mathematical problem, but a gateway to a world of understanding, appreciation, and wonder that awaits us all in the realm of mathematics.

In the spirit of mathematical exploration and the pursuit of knowledge, let us embrace the challenges that lie ahead, armed with the confidence of understanding, the curiosity of discovery, and the passion for learning that defines us as seekers of truth and beauty in the world of mathematics. For in this world of numbers and patterns, we find not just problems to be solved, but opportunities to grow, to learn, and to explore the endless frontiers of human knowledge and understanding.

And so, with the solution to the problem of the sum of numbers between 1 and 100 that are divisible by 6, we come to the realization that mathematics is not just a subject, but a way of thinking, a method of discovery, and a journey of exploration that enriches our lives, broadens our perspectives, and deepens our understanding of the world and our place within it.

Thus, as we conclude our exploration of this mathematical problem, we are reminded that the true beauty of mathematics lies not in its complexity, but in its simplicity; not in its abstractness, but in its concreteness and applicability to the real world; and not in its isolation, but in its interconnectedness with all aspects of human knowledge and experience. And it is this realization, this appreciation for the beauty and utility of mathematics, that will continue to inspire us, to motivate us, and to guide us as we venture forth into the vast and wondrous world of numbers, patterns, and mathematical discovery.

In reflection, the problem of finding the sum of numbers between 1 and 100 that are divisible by 6 has taught us valuable lessons about mathematics, about learning, and about ourselves. It has shown us that even in the simplest of problems, there lies a depth of complexity, a richness of insight, and a beauty of solution that can inspire, educate, and enlighten us. And it is this realization, this awareness, and this appreciation that we will carry with us, not just as we solve mathematical problems, but as we navigate the complexities, challenges, and opportunities of life itself.

For in the end, mathematics is not just about solving problems; it is about understanding the world, about growing as individuals, and about contributing to the greater good. And it is this vision, this passion, and this commitment that will continue to drive us, to inspire us, and to guide us as we explore, discover, and learn in the wondrous world of mathematics.

The journey may end here for this particular problem, but the lessons learned, the insights gained, and the appreciation developed will stay with us, shaping our approach to future challenges, guiding our pursuit of knowledge, and inspiring our love for the beauty, elegance, and simplicity of mathematics. And so, as we move forward, let us remember that every problem solved is not an end, but a new beginning, a fresh start, and an opportunity to explore further into the vast, complex, and beautiful world of mathematics, where every solution holds a secret, every calculation conceals a story, and every pattern waits to be uncovered by curious minds and diligent effort.

In closing, the sum of the numbers between 1 and 100 that are divisible by 6 is a problem that has led us on a journey of discovery, a path of exploration, and a world of wonder. Through its solution, we have gained insights into the beauty of mathematics, the importance of perseverance, and the value of knowledge. And it is these lessons, this appreciation, and this inspiration that will stay with us, guiding us as we continue to explore, to learn, and to cherish the beauty, elegance, and simplicity of mathematics.

The problem may be solved, but the journey of mathematical discovery is endless, filled with challenges to overcome, secrets to uncover, and wonders to behold. And it is this journey, this pursuit of knowledge, and this love for mathematics that will forever change us, inspire us, and guide us as we navigate the complexities and wonders of our world.

In the spirit of this endless journey, let us embrace the challenges, cherish the discoveries, and appreciate the beauty that mathematics has to offer. For in this world of numbers and patterns, we find not just problems to be solved, but opportunities to grow, to learn, and to explore the endless frontiers of human knowledge and understanding. And it is this realization, this awareness, and this appreciation that will forever inspire us, motivate us, and guide us as we venture forth into the vast and wondrous world of mathematics.

And so, with the solution to the problem of the sum of numbers between 1 and 100 that are divisible by 6, we come to the end of one journey, but the beginning of another, a journey that is endless, a path that is winding, and a world that is full of wonder and discovery. For in the world of mathematics, every problem solved is not an end, but a new beginning, a fresh start, and an opportunity to explore further into the vast, complex, and beautiful world of numbers and patterns that surround us, inspire us, and guide us as we continue to learn, to grow, and to cherish the beauty, elegance, and simplicity of mathematics.

The final thought, as we close this chapter on the sum of numbers between 1 and 100 that are divisible by 6, is one of gratitude for the journey, appreciation for the lessons learned, and anticipation for the discoveries yet to come. For in the world of mathematics, every ending marks a new beginning, every solution conceals a new problem, and every pattern waits to be uncovered by curious minds and diligent effort. And it is this realization, this awareness, and this inspiration that will forever guide us, motivate us, and inspire us as we explore, discover, and learn in the wondrous world of mathematics.

In the end, the sum of the numbers between 1 and 100 that are divisible by 6 is 816, a number that represents not just the solution to a mathematical problem, but a gateway to a world of understanding, appreciation, and wonder that awaits us all in the realm of mathematics. And it is this world, this journey, and this pursuit of knowledge that we will continue to cherish, to explore, and to inspire others to discover, as we move forward, forever changed by the beauty, elegance, and simplicity of mathematics.

Let us now summarize the key points of our discussion in a concise manner, using a table to highlight the main elements of the problem and its solution:

Problem Element	Description
Sequence Identification	Identifying the sequence of numbers between 1 and 100 that are divisible by 6.
Number of Terms	Calculating the number of terms in the sequence What is the sum of numbers between 1 and 100 divisible by 6? To find the sum of numbers between 1 and 100 that are divisible by 6, we first need to identify all the numbers within this range that meet the criteria. The numbers divisible by 6 between 1 and 100 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96. This sequence is an arithmetic progression where the first term, a, is 6, and the common difference, d, is also 6. The sum of an arithmetic series can be calculated using the formula: sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. In this case, the first term, a, is 6, the last term, l, is 96, and there are 16 terms in total (since we are counting from 6 to 96, inclusive, with a step of 6). Plugging these values into the formula gives us: sum = 16/2 * (6 + 96) = 8 * 102 = 816. Therefore, the sum of numbers between 1 and 100 that are divisible by 6 is 816. How do I calculate the number of terms in the sequence of numbers divisible by 6 between 1 and 100? Calculating the number of terms in an arithmetic sequence can be done using the formula for the nth term: a_n = a + (n-1)d, where a_n is the nth term, a is the first term, n is the number of terms, and d is the common difference. For the sequence of numbers divisible by 6 between 1 and 100, the first term, a, is 6, and the common difference, d, is also 6. We want to find n when the last term, a_n, is 96. Substituting these values into the formula gives us 96 = 6 + (n-1)6. Solving for n, we get 96 – 6 = (n-1)6, which simplifies to 90 = (n-1)6. Dividing both sides by 6 gives us 15 = n-1. Adding 1 to both sides yields n = 16. Therefore, there are 16 terms in the sequence of numbers divisible by 6 between 1 and 100. This calculation is essential for determining the sum of the sequence, as it is used in the formula for the sum of an arithmetic series. What is the formula for the sum of an arithmetic series, and how does it apply to numbers divisible by 6? The formula for the sum of an arithmetic series is sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. This formula applies to any arithmetic sequence, including the sequence of numbers between 1 and 100 that are divisible by 6. For this specific sequence, we have already identified the first term, a, as 6, the last term, l, as 96, and the number of terms, n, as 16. By substituting these values into the formula, we can calculate the sum of the numbers between 1 and 100 that are divisible by 6. The calculation is as follows: sum = 16/2 * (6 + 96) = 8 * 102 = 816. This demonstrates how the formula for the sum of an arithmetic series can be applied to find the sum of a specific sequence, in this case, the numbers divisible by 6 between 1 and 100. Can I use the formula for the sum of an arithmetic series for sequences with different common differences? Yes, the formula for the sum of an arithmetic series, sum = n/2 * (a + l), is applicable to any arithmetic sequence, regardless of the common difference. The key components are the number of terms (n), the first term (a), and the last term (l), which can be determined for any arithmetic sequence. Whether the common difference is 1, 6, or any other number, the formula remains the same, making it a versatile tool for calculating the sum of various arithmetic sequences. For example, if we were looking at the sequence of numbers divisible by 3 between 1 and 100, the first term would be 3, the last term would be 99, and the common difference would be 3. We would first need to find the number of terms in this sequence using the formula for the nth term of an arithmetic sequence. Once we have all the necessary components (n, a, and l), we can apply the sum formula to find the total sum of the sequence, demonstrating the formula’s applicability to sequences with different common differences. How does the sequence of numbers divisible by 6 relate to other sequences of numbers divisible by other divisors? The sequence of numbers divisible by 6 between 1 and 100 is closely related to other sequences of numbers divisible by different divisors, particularly those that are factors of 6, such as 1, 2, and 3. For instance, every number divisible by 6 is also divisible by 1, 2, and 3, making the sequence of numbers divisible by 6 a subset of the sequences of numbers divisible by 1, 2, and 3. Understanding these relationships can provide insights into the properties of numbers and their divisibility, which is fundamental in number theory. The relationships between sequences of numbers divisible by different divisors can also be useful in solving problems that involve multiple conditions of divisibility. For example, finding the sum of numbers between 1 and 100 that are divisible by both 2 and 3 (which essentially means divisible by 6) requires understanding how the sequences of numbers divisible by 2 and 3 intersect. This intersection is precisely the sequence of numbers divisible by 6, highlighting the importance of recognizing the relationships between different sequences of numbers based on their divisibility. What are the practical applications of calculating the sum of numbers divisible by 6 between 1 and 100? Calculating the sum of numbers divisible by 6 between 1 and 100 may seem like a theoretical exercise, but it has practical applications in various fields, including mathematics education, computer science, and finance. In mathematics education, such calculations help students understand arithmetic sequences and series, which are fundamental concepts in algebra and calculus. In computer science, algorithms for calculating sums of sequences are crucial for solving complex problems efficiently. In finance, understanding sequences and series can help in calculating interest, investments, and other financial metrics over time. Moreover, the ability to calculate the sum of a sequence of numbers divisible by a certain divisor is essential in data analysis, where one might need to sum up values that meet specific criteria, such as sales figures on specific days of the week or month. The concept can also be applied to physics and engineering, where the sum of forces or energies over a period might be necessary for calculations. Thus, while the specific calculation of the sum of numbers divisible by 6 between 1 and 100 might be a niche problem, the underlying principles and techniques have broad applications across multiple disciplines. How can I generalize the method for calculating the sum of numbers divisible by any number between 1 and 100? To generalize the method for calculating the sum of numbers divisible by any number between 1 and 100, you can follow a systematic approach. First, identify the divisor (the number by which the sequence is divisible). Then, determine the first and last terms of the sequence within the range of 1 to 100. The first term will be the divisor itself if it is less than or equal to 100, and the last term will be the largest multiple of the divisor that is less than or equal to 100. Next, calculate the number of terms in the sequence using the formula for the nth term of an arithmetic sequence. Once you have the first term, last term, and the number of terms, you can apply the formula for the sum of an arithmetic series: sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. This approach can be generalized for any divisor, allowing you to calculate the sum of numbers divisible by any number between 1 and 100. For example, to find the sum of numbers divisible by 4, you would identify the sequence (4, 8, 12, …, 100), calculate the number of terms, and then apply the sum formula. This method provides a flexible and systematic way to solve similar problems for different divisors. Categories Tech Guides Leave a Comment Cancel reply Comment Name Email Website Save my name, email, and website in this browser for the next time I comment. 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Problem Element

Description

Sequence Identification

Identifying the sequence of numbers between 1 and 100 that are divisible by 6.

Number of Terms

Calculating the number of terms in the sequence

What is the sum of numbers between 1 and 100 divisible by 6?

To find the sum of numbers between 1 and 100 that are divisible by 6, we first need to identify all the numbers within this range that meet the criteria. The numbers divisible by 6 between 1 and 100 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96. This sequence is an arithmetic progression where the first term, a, is 6, and the common difference, d, is also 6.

The sum of an arithmetic series can be calculated using the formula: sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. In this case, the first term, a, is 6, the last term, l, is 96, and there are 16 terms in total (since we are counting from 6 to 96, inclusive, with a step of 6). Plugging these values into the formula gives us: sum = 16/2 * (6 + 96) = 8 * 102 = 816. Therefore, the sum of numbers between 1 and 100 that are divisible by 6 is 816.

How do I calculate the number of terms in the sequence of numbers divisible by 6 between 1 and 100?

Calculating the number of terms in an arithmetic sequence can be done using the formula for the nth term: a_n = a + (n-1)d, where a_n is the nth term, a is the first term, n is the number of terms, and d is the common difference. For the sequence of numbers divisible by 6 between 1 and 100, the first term, a, is 6, and the common difference, d, is also 6. We want to find n when the last term, a_n, is 96. Substituting these values into the formula gives us 96 = 6 + (n-1)6.

Solving for n, we get 96 – 6 = (n-1)6, which simplifies to 90 = (n-1)6. Dividing both sides by 6 gives us 15 = n-1. Adding 1 to both sides yields n = 16. Therefore, there are 16 terms in the sequence of numbers divisible by 6 between 1 and 100. This calculation is essential for determining the sum of the sequence, as it is used in the formula for the sum of an arithmetic series.

What is the formula for the sum of an arithmetic series, and how does it apply to numbers divisible by 6?

The formula for the sum of an arithmetic series is sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. This formula applies to any arithmetic sequence, including the sequence of numbers between 1 and 100 that are divisible by 6. For this specific sequence, we have already identified the first term, a, as 6, the last term, l, as 96, and the number of terms, n, as 16.

By substituting these values into the formula, we can calculate the sum of the numbers between 1 and 100 that are divisible by 6. The calculation is as follows: sum = 16/2 * (6 + 96) = 8 * 102 = 816. This demonstrates how the formula for the sum of an arithmetic series can be applied to find the sum of a specific sequence, in this case, the numbers divisible by 6 between 1 and 100.

Can I use the formula for the sum of an arithmetic series for sequences with different common differences?

Yes, the formula for the sum of an arithmetic series, sum = n/2 * (a + l), is applicable to any arithmetic sequence, regardless of the common difference. The key components are the number of terms (n), the first term (a), and the last term (l), which can be determined for any arithmetic sequence. Whether the common difference is 1, 6, or any other number, the formula remains the same, making it a versatile tool for calculating the sum of various arithmetic sequences.

For example, if we were looking at the sequence of numbers divisible by 3 between 1 and 100, the first term would be 3, the last term would be 99, and the common difference would be 3. We would first need to find the number of terms in this sequence using the formula for the nth term of an arithmetic sequence. Once we have all the necessary components (n, a, and l), we can apply the sum formula to find the total sum of the sequence, demonstrating the formula’s applicability to sequences with different common differences.

How does the sequence of numbers divisible by 6 relate to other sequences of numbers divisible by other divisors?

The sequence of numbers divisible by 6 between 1 and 100 is closely related to other sequences of numbers divisible by different divisors, particularly those that are factors of 6, such as 1, 2, and 3. For instance, every number divisible by 6 is also divisible by 1, 2, and 3, making the sequence of numbers divisible by 6 a subset of the sequences of numbers divisible by 1, 2, and 3. Understanding these relationships can provide insights into the properties of numbers and their divisibility, which is fundamental in number theory.

The relationships between sequences of numbers divisible by different divisors can also be useful in solving problems that involve multiple conditions of divisibility. For example, finding the sum of numbers between 1 and 100 that are divisible by both 2 and 3 (which essentially means divisible by 6) requires understanding how the sequences of numbers divisible by 2 and 3 intersect. This intersection is precisely the sequence of numbers divisible by 6, highlighting the importance of recognizing the relationships between different sequences of numbers based on their divisibility.

What are the practical applications of calculating the sum of numbers divisible by 6 between 1 and 100?

Calculating the sum of numbers divisible by 6 between 1 and 100 may seem like a theoretical exercise, but it has practical applications in various fields, including mathematics education, computer science, and finance. In mathematics education, such calculations help students understand arithmetic sequences and series, which are fundamental concepts in algebra and calculus. In computer science, algorithms for calculating sums of sequences are crucial for solving complex problems efficiently. In finance, understanding sequences and series can help in calculating interest, investments, and other financial metrics over time.

Moreover, the ability to calculate the sum of a sequence of numbers divisible by a certain divisor is essential in data analysis, where one might need to sum up values that meet specific criteria, such as sales figures on specific days of the week or month. The concept can also be applied to physics and engineering, where the sum of forces or energies over a period might be necessary for calculations. Thus, while the specific calculation of the sum of numbers divisible by 6 between 1 and 100 might be a niche problem, the underlying principles and techniques have broad applications across multiple disciplines.

How can I generalize the method for calculating the sum of numbers divisible by any number between 1 and 100?

To generalize the method for calculating the sum of numbers divisible by any number between 1 and 100, you can follow a systematic approach. First, identify the divisor (the number by which the sequence is divisible). Then, determine the first and last terms of the sequence within the range of 1 to 100. The first term will be the divisor itself if it is less than or equal to 100, and the last term will be the largest multiple of the divisor that is less than or equal to 100. Next, calculate the number of terms in the sequence using the formula for the nth term of an arithmetic sequence.

Once you have the first term, last term, and the number of terms, you can apply the formula for the sum of an arithmetic series: sum = n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term. This approach can be generalized for any divisor, allowing you to calculate the sum of numbers divisible by any number between 1 and 100. For example, to find the sum of numbers divisible by 4, you would identify the sequence (4, 8, 12, …, 100), calculate the number of terms, and then apply the sum formula. This method provides a flexible and systematic way to solve similar problems for different divisors.