Sequences and Patterns

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What is a sequence?

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

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What is a term in a sequence?

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A term is an individual number in a sequence.

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence 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 in which 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 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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How do you find 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 a pattern in mathematics?

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A pattern is a repeated or recurring sequence of numbers or shapes that follows a specific rule.

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What is the common difference in an arithmetic sequence?

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The common difference is the amount added to each term to get the next term in an arithmetic sequence.

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What is the common ratio in a geometric sequence?

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The common ratio is the factor by which each term is multiplied to get the next term in a geometric sequence.

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How can you determine if a sequence is arithmetic, geometric, or neither?

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To determine the type of sequence, check the differences between terms (arithmetic) or the ratios of consecutive terms (geometric). If neither is consistent, it is neither.