Arithmetic Sequences

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What is an arithmetic sequence?

Back

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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What is the common difference in an arithmetic sequence?

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The common difference is the fixed amount added to each term to get the next term in the sequence.

Tags

CCSS.HSF.BF.A.2

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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

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The 4th term is 5 + 3(4-1) = 5 + 9 = 14.

Tags

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 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)), where a(n) is the nth term.

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Given the sequence 10, 7, 4, 1, what is the common difference?

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The common difference is -3.

Tags

CCSS.HSF.BF.A.2

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If c(1) = 6 and c(n) = c(n-1) - 16, what is c(3)?

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c(3) = c(2) - 16 = (c(1) - 16) - 16 = 6 - 32 = -26.

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CCSS.HSF.IF.A.3

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What is the next term in the sequence 7, 5, 3?

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The next term is 1.

Tags

CCSS.HSF.BF.A.2

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If a(n) = -6 + 3(n-1), what is a(16)?

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a(16) = -6 + 3(16-1) = -6 + 45 = 39.

Tags

CCSS.HSF.BF.A.2

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What is the next term in the sequence 2, -1, -4, -7, -10?

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The next term is -13.

Tags

CCSS.HSF.BF.A.2