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**Arithmetic Sequences and Series**

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Arithmetic Sequences

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An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms.

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**Which of the following sequences are arithmetic**

Which of the following sequences are arithmetic? Identify the common difference. YES YES NO NO YES

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The common difference is always the difference between any term and the term that proceeds that term. Common Difference = 5

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**The general form of an ARITHMETIC sequence.**

First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

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**Formula for the nth term of an ARITHMETIC sequence.**

If we know any three of these we ought to be able to find the fourth.

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Given: Find: IDENTIFY SOLVE

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**Find: What term number is -169?**

Given: Find: What term number is -169? IDENTIFY SOLVE

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Given: Find: What’s the real question? The Difference IDENTIFY SOLVE

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Given: Find: IDENTIFY SOLVE

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Arithmetic Series

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**Write the first three terms and the last two terms of the following arithmetic series.**

What is the sum of this series?

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**What is the SUM of these terms?**

Written 1st to last. Written last to 1st. Add Down 50 Terms 71 + (-27) Each sum is the same.

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In General . . .

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**Find the sum of the terms of this arithmetic series.**

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**Find the sum of the terms of this arithmetic series.**

What term is -5?

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**Alternate formula for the sum of an Arithmetic Series.**

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**Find the sum of this series**

It is not convenient to find the last term.

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Your Turn

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