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

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December 22, 2015
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Worked example: arithmetic series (sum expression) | High School Math | Khan Academy

## 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.

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### 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.