Worked example: arithmetic series (sum expression) | High School Math | Khan Academy | Summary and Q&A

TL;DR

Learn how to calculate the sum of an arithmetic series by finding the first term, the last term, and the number of terms.

Key Insights

• 🍉 The given arithmetic series involves adding 6 to each term, creating a constant difference.
• 🍉 The sum is calculated by finding the first term, the last term, and the number of terms, and then using the sum formula.
• ❓ Sigma notation can be used to represent an arithmetic series concisely.
• ⏫ It is important to double-check calculations and formulas to avoid errors.
• 🌍 The concept of arithmetic series is fundamental in mathematics and has various real-world applications.
• 🇨🇷 The sum of an arithmetic series can be used to solve problems such as finding the total cost of multiple transactions with a fixed cost increase.
• ❎ Arithmetic series can have both positive and negative common differences, depending on the situation.

Transcript

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Questions & Answers

Q: What is an arithmetic series?

An arithmetic series is a series of numbers in which each term is obtained by adding a fixed constant (common difference) to the previous term.

Q: How do you calculate the sum of an arithmetic series?

To calculate the sum of an arithmetic series, you need to find the first term (a1), the last term (a-sub-n), and the number of terms (n). Then, use the formula: sum = (a1 + a-sub-n) * n / 2.

Q: How do you find the number of terms in an arithmetic series?

To find the number of terms in an arithmetic series, subtract the first term from the last term and divide by the common difference. In this example, (2044 - (-50)) / 6 = 349.

Q: Why is there a plus 1 in the equation for the number of terms?

The plus 1 accounts for the inclusion of the first term in the series. Even though we calculated 349 terms by adding the common difference, we have to include the first term as well.

Summary & Key Takeaways

• The given content explains how to calculate the sum of an arithmetic series.

• The series is formed by adding 6 to each successive term.

• The first term is -50, the last term is 2044, and there are 350 terms in total.