Arithmetic and Geometric Sequences

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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How do you find the common difference in an arithmetic sequence?

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The common difference can be found by subtracting any term from the subsequent term. For example, in the sequence 5, 8, 11, the common difference is 8 - 5 = 3.

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How do you find the common ratio in a geometric sequence?

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The common ratio can be found by dividing any term by the previous term. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 3.

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Identify the common difference in the sequence: 10, 7, 4, 1, ...

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The common difference is -3.

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Identify the common ratio in the sequence: 3, 9, 27, 81, ...

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The common ratio is 3.

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What is the formula for the nth term of an arithmetic sequence?

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What is the formula for the nth term of a geometric sequence?

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What type of sequence is represented by the series: 1, 4, 9, 16, ...?

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This is neither an arithmetic nor a geometric sequence; it is a sequence of perfect squares.

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What is the sum of the first n terms of an arithmetic sequence?

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