Sum of All Multiples of 7 Less Than 100: An SEO-Optimized Guide

Understanding and calculating the sum of all multiples of 7 that are less than 100 can be both an educational exercise and a practical tool. This guide provides a comprehensive explanation, along with an optimized content structure and relevant keywords to help improve search engine rankings.

Understanding Multiples of 7

Multiples of 7 are numbers that can be obtained by multiplying 7 by an integer. For example, 7, 14, 21, and so on are multiples of 7. The task here is to find the sum of all such multiples that are less than 100.

Counting the Multiples of 7

To start, let's count the multiples of 7 between 1 and 100:

Count of Multiples: 100 / 7 14

This means there are 14 multiples of 7 in the range from 1 to 100. These multiples are:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98

These are the first 14 terms of the arithmetic sequence where the first term (a) is 7 and the common difference (d) is also 7.

Sum of an Arithmetic Sequence

The sum of an arithmetic sequence can be calculated using the formula:

Sum (S) (n/2) * (a l)

where n is the number of terms, a is the first term, and l is the last term.

In our case:

n 14 (number of multiples) a 7 (first multiple) l 98 (last multiple)

Substituting these values into the formula:

S (14/2) * (7 98)

S 7 * 105

S 735

Thus, the sum of all multiples of 7 that are less than 100 is 735.

Optimized Content for SEO

For SEO optimization, it's important to include relevant keywords, meta tags, and structured data. Here are some key elements to include:

Meta Title: "Sum of All Multiples of 7 Less Than 100: Easy Calculation with Steps" Description: "Learn how to calculate the sum of all multiples of 7 that are less than 100. This guide explains the arithmetic sequence and provides a step-by-step solution." Keywords: multiples of 7, sum calculation, arithmetic series

Conclusion

Capturing the sum of all multiples of 7 less than 100 is a straightforward task once you understand the arithmetic sequence and apply the appropriate formula. By breaking down the steps and using clear, concise language, you can create a high-quality, SEO-friendly content that ranks well on search engine results pages.

Frequently Asked Questions (FAQs)

Q: What is a multiple of 7?
A: A multiple of 7 is any number that can be expressed as 7 multiplied by an integer. Examples include 7, 14, 21, 28, etc. Q: How do you find the sum of multiples of 7?
A: Use the arithmetic sequence formula: Sum (S) (n/2) * (a l), where n is the number of multiples, a is the first multiple, and l is the last multiple. Q: Why is it important to know the sum of multiples?
A: Knowing how to calculate the sum of multiples is useful in various mathematical and practical applications, such as finance, engineering, and problem-solving in mathematics.

By mastering this concept, you can enhance your mathematical skills and improve your SEO ranking with quality content.