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More Lessons for Grade 9

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Videos, solutions, examples, worksheets, games and activities to help Algebra II students learn about arithmetic series.

**Arithmetic Series**

We can use what we know of arithmetic sequences to understand arithmetic series. An arithmetic series is a series or summation that sums the terms of an arithmetic sequence. There are methods and formulas we can use to find the value of an arithmetic series. Understanding arithmetic series can help to understand geometric series, and both concepts will be used when learning more complex Calculus topics.

**What is an Arithmetic Series?**

Define a series.

Determine the partial sum of an arithmetic series.

Summing or adding the terms of an arithmetic sequence creates what is called a series.

Examples:

Determine the sum of the arithmetic series.

1. 3 + 8 + 13 + ... 73 2. a_{n} = -4n + 3; n = 20

**Deriving the formula for the sum of an arithmetic series based on an example.**

Example:

A theater has 50rows of seats. There are 18 seats in the first row, 20 seats in the second, 22 in the third and so on.

**Finding the Sum of a Finite Arithmetic Series**

This video shows two formulas to find the sum of a finite arithmetic series and does two examples of finding some sums The sun, S_{n}, of the first n terms of an arithmetic series with a_{n} = a_{1} + (n -1)d is

S_{n} = n(a_{1} + a_{n})/2

Example:

Consider the arithmetic sequence

2,5,8,11,14,17, ...

a) Find the sum of the first 10 terms.

b) Find the sum of the series starting with the 11th term and ending with the 28th term.

**What is the difference between a sequence and a series?**

Gives formula for finding the sum of the first "n" terms of a series, and relating the two formulae used.**How to find the sum of an arithmetic series?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 9

Math Worksheets

Videos, solutions, examples, worksheets, games and activities to help Algebra II students learn about arithmetic series.

We can use what we know of arithmetic sequences to understand arithmetic series. An arithmetic series is a series or summation that sums the terms of an arithmetic sequence. There are methods and formulas we can use to find the value of an arithmetic series. Understanding arithmetic series can help to understand geometric series, and both concepts will be used when learning more complex Calculus topics.

Define a series.

Determine the partial sum of an arithmetic series.

Summing or adding the terms of an arithmetic sequence creates what is called a series.

Examples:

Determine the sum of the arithmetic series.

1. 3 + 8 + 13 + ... 73 2. a

Example:

A theater has 50rows of seats. There are 18 seats in the first row, 20 seats in the second, 22 in the third and so on.

This video shows two formulas to find the sum of a finite arithmetic series and does two examples of finding some sums The sun, S

S

Example:

Consider the arithmetic sequence

2,5,8,11,14,17, ...

a) Find the sum of the first 10 terms.

b) Find the sum of the series starting with the 11th term and ending with the 28th term.

Gives formula for finding the sum of the first "n" terms of a series, and relating the two formulae used.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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