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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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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.

Tags

CCSS.HSF.BF.A.2

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What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

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Given a_1 = 5 and d = 3, what is a_4?

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a_4 = 5 + (4-1)3 = 5 + 9 = 14.

Tags

CCSS.HSF.BF.A.2

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What is a convergent sequence?

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A convergent sequence is a sequence of numbers that approaches a specific value as the number of terms increases.

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What is a divergent sequence?

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A divergent sequence is a sequence that does not approach a specific value; it may increase or decrease without bound.

Tags

CCSS.HSF.BF.A.2

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How do you determine if a sequence converges or diverges?

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To determine convergence or divergence, analyze the behavior of the sequence as n approaches infinity.

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What is the explicit formula for the sequence 2, 8, 14, ...?

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The explicit formula is a_n = 6n - 4.

Tags

CCSS.HSF.BF.A.2

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If the 6th term of an arithmetic sequence is -38 and the 14th term is -110, what is the explicit rule?

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The explicit rule is a_n = 7 - 9(n - 1).

Tags

CCSS.HSF.BF.A.2

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What is the formula for the sum of the first n terms of an arithmetic sequence?

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The sum S_n of the first n terms is given by S_n = n/2 * (a_1 + a_n).