Sequence

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What is a sequence?

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

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What is the difference between a finite and an infinite sequence?

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A finite sequence has a limited number of terms, while an infinite sequence continues indefinitely.

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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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What is a pattern in a sequence?

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A pattern in a sequence is a recognizable and predictable arrangement of numbers or events.

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence 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 of a geometric sequence 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 recursive sequence?

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A recursive sequence is a sequence in which each term is defined as a function of the preceding terms.

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What is a Fibonacci sequence?

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A Fibonacci sequence is a specific sequence where each term is the sum of the two preceding ones, usually starting with 0 and 1.

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What is a series?

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A series is the sum of the terms of a sequence.