Arithmetic Sequences

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What is the common difference in an arithmetic sequence?

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The common difference (d) is the distance from one term to the next 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 and d is the common difference.

Tags

CCSS.HSF.BF.A.2

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What is the first term of the arithmetic sequence: 5, 8, 11, ...?

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The first term (a_1) is 5.

Tags

CCSS.HSF.BF.A.2

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If the common difference of an arithmetic sequence is -2, what is the second term if the first term is 10?

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The second term is 8 (10 + (-2)).

Tags

CCSS.HSF.BF.A.2

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What is the 10th term of the arithmetic sequence: 2, 5, 8, ...?

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The 10th term is 29.

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 to solve for n.

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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What is the 5th term of the arithmetic sequence: 4, 9, 14, ...?

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The 5th term is 24.

Tags

CCSS.HSF.BF.A.2

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In the sequence 12, 9, 6, ..., 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 the 15th term of an arithmetic sequence is 50 and the common difference is 2, what is the first term?

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The first term is 20.

Tags

CCSS.HSF.BF.A.2