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. For example, 2, 4, 6, 8, ... has a common difference of 2.

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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. For example, 3, 6, 12, 24, ... has a common ratio of 2.

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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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How do you identify an arithmetic sequence?

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To identify an arithmetic sequence, check if the difference between consecutive terms is constant. If it is, the sequence is arithmetic.

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How do you identify a geometric sequence?

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To identify a geometric sequence, check if the ratio of consecutive terms is constant. If it is, the sequence is geometric.

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What is a common difference in an arithmetic sequence?

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The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence. For example, in the sequence 5, 8, 11, the common difference is 3.

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What is a common ratio in a geometric sequence?

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The common ratio is the fixed amount multiplied to each term to get the next term in a geometric sequence. For example, in the sequence 2, 6, 18, the common ratio is 3.

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What is the first term of the sequence 7, 14, 28, 56, ...?

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The first term of the sequence is 7.

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What is the recursive formula for the sequence 7, 14, 28, 56, ...?

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