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What is a sequence in mathematics?

Back

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

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What is the common difference (d) in an arithmetic sequence?

Back

The common difference (d) is the constant amount that each term in the sequence increases or decreases by.

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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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What is the first term (a_1) of the sequence 10, 5, 0, -5, -10?

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The first term (a_1) is 10.

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What is the common difference (d) of the sequence 10, 5, 0, -5, -10?

Back

The common difference (d) is -5.

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What is an explicit formula for a sequence?

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An explicit formula expresses the nth term of a sequence as a function of n.

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What is the explicit formula for the sequence 2, 8, 14, 20?

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The explicit formula is a_n = 6n - 4.

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How do you determine the number of line segments in a geometric pattern?

Back

Count the number of segments added at each step, which often follows a specific rule or pattern.

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What is the formula for the nth term of the sequence -4, -1, 2, 5, 8?

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The formula is a_n = 3n - 4.

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What is a recursive formula for a sequence?

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A recursive formula defines each term of a sequence using the previous term(s).