12/5 Algebra - Applications of Exponential Functions Review

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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 in the sequence 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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What does it mean to reflect a function across the x-axis?

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Reflecting a function across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

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What is the significance of the first term in a geometric sequence?

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The first term (a_1) is crucial as it serves as the starting point for generating all subsequent terms in the sequence.

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How do you determine if a sequence is geometric?

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A sequence is geometric if the ratio between consecutive terms is constant.

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What is the common ratio for the sequence 3, -12, 48, -192?

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The common ratio is -4, found by dividing -12 by 3.

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What is the explicit formula for the geometric sequence with first term 3 and common ratio -4?

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How do you write the explicit formula for a geometric sequence given the first term and common ratio?

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Front

What is the common ratio for the sequence 162, 108, 72, 48?

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