Arithmetic Sequences

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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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What is the common difference in an arithmetic sequence?

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

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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, d is the common difference, and n is the term number.

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CCSS.HSF.BF.A.2

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Is the sequence 5, 4.25, 3.5, 2.75 an arithmetic sequence?

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Yes, the common difference is -0.75.

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CCSS.HSF.BF.A.2

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Find the 32nd term of the sequence 34, 37, 40, 43, ...

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The 32nd term is 127.

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CCSS.HSF.BF.A.2

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Identify the common difference in the sequence 3, 7, 11, 15, ...

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The common difference is 4.

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CCSS.HSF.BF.A.2

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What are the next two terms of the sequence 4, 7, 10, 13?

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The next two terms are 16 and 19.

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CCSS.HSF.BF.A.2

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Find the 32nd term of the sequence 9, 4, -1, -6, -11, ...

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The 32nd term is -146.

Tags

CCSS.HSF.BF.A.2

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If the first term of an arithmetic sequence is 10 and the common difference is 2, what is the 5th term?

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The 5th term is 18.

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 = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.