Geometric Series Review

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What is a geometric series?

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A geometric series is the expression formed by adding the terms of a geometric sequence.

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What is the formula for the sum of an infinite geometric series?

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The sum S of an infinite geometric series can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio (|r| < 1).

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10

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What is the common ratio in a geometric sequence?

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The common ratio is the factor by which each term in the sequence is multiplied to get the next term.

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Convergent.

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If a culture of bacteria doubles every 2 hours, how many will there be after 12 hours starting with 200?

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12600.

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8.

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What is the sum of the first n terms of a geometric series?

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The sum S_n of the first n terms can be calculated using S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

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What does it mean for a series to diverge?

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A series diverges if the sum of its terms does not approach a finite limit.

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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 can be calculated using a_n = a * r^(n-1), where a is the first term and r is the common ratio.