Sequences - Recursive Formulas

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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 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 determine if a sequence is arithmetic?

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To determine if a sequence is arithmetic, calculate the difference between consecutive terms. If the difference is constant, it is arithmetic.

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How do you determine if a sequence is geometric?

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

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What is the 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.

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

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The nth term (a_n) of an arithmetic sequence can be calculated 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 (a_n) of a geometric sequence can be calculated 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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Identify the common ratio for the geometric sequence: 2, 6, 18, 54, ...

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The common ratio is 3.

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Identify the common difference for the arithmetic sequence: 5, 10, 15, 20, ...

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The common difference is 5.