Understanding the Sum of All Integers from 45 to 155

Are you looking to calculate the sum of all integers from 45 to 155? This is a common problem that often appears in math competitions, academic exams, and even in programming. In this article, we'll explore a method not only to solve this problem but also discuss the important role of understanding the sum of integers in SEO optimization for tech and educational content.

The Formula: Sum of an Arithmetic Series

When dealing with a series of numbers (in this case, integers), the sum is quite straightforward if we apply the formula for the sum of an arithmetic series. The formula is:

Sum (n/2) * (a l)

Where:

n is the number of terms in the series, a is the first term of the series, l is the last term of the series.

Let's break down how to use this formula step-by-step.

Step-by-Step Guide to Solve the Problem

1. Identify the terms: The series starts at 45 and ends at 155.

2. Calculate the number of terms: The number of terms in the series is given by (155 - 45 1) 111 terms.

3. Apply the formula:

Sum (111/2) * (45 155)

4. Perform the calculation:

Sum (111/2) * 200 55.5 * 200 11100

So, the sum of all integers from 45 to 155 inclusive is 11100.

A Visual Breakdown

To better understand the process, let's use a visual representation. Imagine the number line from 45 to 155:

A number line representation from 45 to 155.

As illustrated, from 45 to 155, there are 111 integers.

Relevance to SEO and Audience Engagement

Understanding the sum of integers is not just about solving problems but also about enhancing your content's SEO for technical and educational websites. Here's why this topic is relevant:

Use of Specific Keywords: Incorporating specific keywords like 'sum of integers 45-155' can improve search engine rankings. Providing Value: By offering step-by-step solutions and visual aids, you keep your audience engaged and likely to stay on your site longer, which is a ranking factor. Hours of Engagement: Content that answers specific questions can significantly increase the time users spend on your site, improving user engagement metrics.

Example Meta Descriptions for SEO

To optimize your content, consider these meta descriptions:

"Learn how to find the sum of integers from 45 to 155 with a step-by-step guide. Discover the formula and practice with examples!" "Solve the sum of integers from 45 to 155 using the arithmetic series formula. Get a detailed walkthrough and tips for your next math challenge!" "Explore the method of calculating the sum of integers from 45 to 155. Understand the process and apply the arithmetic series formula effectively!"

Conclusion

In summary, understanding the sum of integers is crucial for both educational and SEO purposes. Applying the arithmetic series formula not only solves the problem efficiently but also enhances the visibility and engagement of your content online. Remember to integrate specific keywords, provide value, and improve your website's SEO to attract more readers and improve your site's ranking.