Geometric Sequences: Graphing & Word Problems

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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, i.e., r = a_n / a_(n-1).

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What is the explicit formula for a geometric sequence?

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How do you graph a geometric sequence?

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To graph a geometric sequence, plot the terms of the sequence on a coordinate plane, with the term number (n) on the x-axis and the term value (a_n) on the y-axis.

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The first term (a_1) is 4, as it is found by substituting n=1 into the formula.

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If a geometric sequence starts with 729 and has a common ratio of 1/3, what is the second term?

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What is the sum of the first n terms of a geometric 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 of consecutive terms is constant.

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What is the explicit formula for the sequence where the first term is 2 and the common ratio is 3?

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