Sequences

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What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

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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.

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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 is found by subtracting any term from the term that follows it.

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

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The common ratio is found by dividing any term by the term that precedes it.

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

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The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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

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The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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What is the next term in the sequence 2, 4, 6, 8,...?

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The next term is 10, as the common difference is 2.

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What is the next term in the sequence 3, 9, 27,...?

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The next term is 81, as the common ratio is 3.

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How do you identify if a sequence is arithmetic or geometric?

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Check if the difference between terms is constant (arithmetic) or if the ratio between terms is constant (geometric).