Understanding Arithmetic Sequences

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Common difference (arithmetic sequence)

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fixed amount added to each term to get the next term.

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Arithmetic sequence

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sequence where each term is found by adding the common difference to the previous term.

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Series

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sum of the terms of a sequence.

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latex="a_n = a_1 + (n-1)d">

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latex="S_n = \frac{n}{2}[2a_1 + (n-1)d]">

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latex="d = 3">

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latex="a_6 = 4 + (6-1) \times 3 = 19">

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latex="S_5 = \frac{5}{2}[2 \times 1 + (5-1) \times 3] = 35">

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True/False: The common difference in an arithmetic sequence can be negative.

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True