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

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The sum of the first n terms (S_n) can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

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

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The 10th term is 5 + (10-1) * 2 = 23.

Tags

CCSS.HSF.BF.A.2

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What is the common difference in the sequence 3, 7, 11, 15?

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The common difference is 4.

Tags

CCSS.HSF.BF.A.2

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What is the difference between two terms in an arithmetic sequence called?

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It is called the common difference.

Tags

CCSS.HSF.BF.A.2

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If the sequence is 10, 15, 20, 25, what will be the 6th term?

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The 6th term will be 10 + (6-1) * 5 = 35.

Tags

CCSS.HSF.BF.A.2

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Which of the following is an arithmetic sequence: 2, 4, 6, 8 or 1, 2, 4, 8?

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2, 4, 6, 8 is an arithmetic sequence because the difference between consecutive terms is constant (2).

Tags

CCSS.HSF.BF.A.2

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What is the 5th term of the arithmetic sequence 1, 4, 7, 10?

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The 5th term is 1 + (5-1) * 3 = 13.

Tags

CCSS.HSF.BF.A.2