Arithmetic Sequences and Series

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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.

Arithmetic Sequences and Series:

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

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

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

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Given: IDENTIFY SOLVE Find:

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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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Written 1st to last. Written last to 1st. What is the SUM of these terms? Add Down 71 + (-27) Each sum is the same. 50 Terms

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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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