U4D2 Explicit & Recursive Geometric Sequences

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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 ratio in a geometric sequence?

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The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

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What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is given by: 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 recursive formula for a geometric sequence?

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The recursive formula for a geometric sequence is: a_n = a_(n-1) * r, with a_1 defined as the first term.

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Identify the common ratio in the sequence: 2, 6, 18, 54,...

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The common ratio is 3, since each term is multiplied by 3 to get the next term.

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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, known as the common difference.

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How do you find the common difference in an arithmetic sequence?

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The common difference (d) can be found by subtracting any term from the next term: d = a_n - a_(n-1).

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What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is given by: 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 recursive formula for an arithmetic sequence?

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The recursive formula for an arithmetic sequence is: a_n = a_(n-1) + d, with a_1 defined as the first term.

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Determine the next three terms in the geometric sequence: 81, 27, 9,...

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The next three terms are 3, 1, and 1/3.