Sequences & Series HPC Review

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What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Tags

CCSS.HSF.BF.A.2

Front

What is a series?

Back

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

Tags

CCSS.HSA.SSE.B.4

Front

Define convergence in the context of sequences.

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A sequence converges if its terms approach a specific value as the number of terms increases.

Front

Define divergence in the context of sequences.

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A sequence diverges if its terms do not approach a specific value as the number of terms increases.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for an arithmetic sequence?

Back

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.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

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The common difference is the difference between consecutive terms in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

Front

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

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The nth term of a geometric sequence 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

Front

What is the sum of the first n terms of an arithmetic series?

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The sum of the first n terms of an arithmetic series is given by: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

What is the formula for the sum of a geometric series?

Back

The sum of the first n terms of a geometric series is given by: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio.

Tags

CCSS.HSA.SSE.B.4

Front

What is the formula for the sum of the first n odd numbers?

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The sum of the first n odd numbers is given by: S_n = n^2.