Explicit Arithmetic Sequences

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What is an explicit arithmetic sequence?

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An explicit arithmetic sequence is a sequence of numbers in which each term is defined by a formula that directly calculates the term based on its position (n) in the sequence.

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

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The formula for the nth term (a_n) of an arithmetic sequence is a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

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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. For example, d = a_2 - a_1.

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Given the sequence 5, 8, 11, 14, ..., what is the common difference?

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The common difference is 3.

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Write the explicit rule for the arithmetic sequence 3, 7, 11, 15,...

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a_n = 4n - 1.

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What are the first term (a_1) and common difference (d) for the sequence 10, 15, 20, 25,...?

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a_1 = 10 and d = 5.

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If the first term of an arithmetic sequence is 2 and the common difference is 4, what is the 5th term?

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The 5th term is 18.

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What is the 10th term of the arithmetic sequence defined by a_n = 3n + 2?

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The 10th term is 32.

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How do you find the next term in the sequence 20, 15, 10, 5,...?

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The next term is 0, found by subtracting the common difference of -5.

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What is the explicit rule for the arithmetic sequence -1, 2, 5, 8,...?

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a_n = 3n - 4.