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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How do you find the common difference in an arithmetic sequence?

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The common difference (d) is found by subtracting any term from the subsequent term in the sequence.

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CCSS.HSF.BF.A.2

Front

What is the formula for the n-th term of an arithmetic sequence?

Back

The n-th term (a_n) of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

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CCSS.HSF.BF.A.2

Front

Is the sequence 2, 4, 6, 8, ... arithmetic?

Back

Yes, the sequence is arithmetic with a common difference of 2.

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CCSS.HSF.BF.A.2

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

Back

The common difference is -3.

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CCSS.HSF.BF.A.2

Front

Can a sequence be arithmetic if the common difference is zero?

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Yes, a sequence can be arithmetic with a common difference of zero; it would consist of the same repeated number.

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CCSS.HSF.BF.A.2

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What is the explicit formula for the arithmetic sequence 5, 10, 15, ...?

Back

The explicit formula is a_n = 5 + (n - 1)5.

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CCSS.HSF.BF.A.2

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How can you determine if a sequence is arithmetic?

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To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant.

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CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence 100, 90, 80, ...?

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The common difference is -10.

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CCSS.HSF.BF.A.2

Front

Is the sequence 1, 2, 4, 8, ... arithmetic?

Back

No, the sequence is not arithmetic; it is geometric.

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CCSS.HSF.BF.A.2