Understanding Arithmetic Sequences

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Arithmetic sequence

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with a constant difference between consecutive terms

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Common difference

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fixed amount added to each term to get the next term

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initial term of an arithmetic sequence

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General term formula

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

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latex="a_5 = 3 + (5-1) \times 2 = 11">

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Sequence: 4, 7, 10, 13, ...

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Arithmetic progression

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name for arithmetic sequence

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latex="a_4 = 10 + (4-1) \times (-2) = 4">

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

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latex="S_6 = \frac{6}{2}[2 \times 5 + (6-1) \times 3] = 63">