Arithmetic Sequence

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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 (d) 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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How do you find the common difference in a sequence?

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To find the common difference, subtract the first term from the second term (d = a2 - a1).

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 second term?

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The second term is 8 (5 + 3).

Tags

CCSS.HSF.BF.A.2

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What is the formula for the nth term of an arithmetic sequence?

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The nth term (an) can be calculated using the formula: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

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Find the 10th term of the arithmetic sequence 4, 7, 10, 13, ...

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The 10th term is 34.

Tags

CCSS.HSF.BF.A.2

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What is the common difference of the sequence 10, 7, 4, 1, ...?

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The common difference is -3.

Tags

CCSS.HSF.BF.A.2

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If the common difference of an arithmetic sequence is 2 and the first term is 1, what is the 5th term?

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The 5th term is 9.

Tags

CCSS.HSF.BF.A.2

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How do you determine the number of terms in an arithmetic sequence?

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You can determine the number of terms by rearranging the nth term formula: n = (an - a1)/d + 1.

Tags

CCSS.HSF.BF.A.2

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

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The sum (S) can be calculated using the formula: S = n/2 * (a1 + an).