Sequences and Series

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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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CCSS.HSF.BF.A.2

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What is a series?

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A series is the sum of the terms of a sequence.

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CCSS.HSA.SSE.B.4

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Define common difference in an arithmetic sequence.

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The common difference is the constant amount that each term in an arithmetic sequence differs from the previous term.

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CCSS.HSF.BF.A.2

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How do you find the nth term of an arithmetic sequence?

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The nth term can be found 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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CCSS.HSF.BF.A.2

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What is a geometric sequence?

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A geometric sequence is a sequence 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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CCSS.HSF.BF.A.2

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Define common ratio in a geometric sequence.

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The common ratio is the constant factor between consecutive terms in a geometric sequence.

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CCSS.HSF.BF.A.2

Front

How do you find the nth term of a geometric sequence?

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The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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What is an infinite geometric series?

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An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely.

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When does an infinite geometric series converge?

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An infinite geometric series converges if the absolute value of the common ratio is less than 1 (|r| < 1).

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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.