Arithmetic Sequences - Explicit Formulas

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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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What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

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How do you find the nth term of an arithmetic sequence?

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To find the nth term of an arithmetic sequence, use the explicit formula: a_n = a_1 + (n - 1)d.

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What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

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Given the first term and common difference, how can you write the explicit formula for an arithmetic sequence?

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If the first term is a_1 and the common difference is d, the explicit formula is a_n = a_1 + (n - 1)d.

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How do you determine the common difference from a sequence?

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To determine the common difference, subtract any term from the subsequent term in the sequence.

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What is the 15th term of the sequence defined by a_n = -3n + 50?

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The 15th term is 5.

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How do you derive the explicit formula from a given arithmetic sequence?

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Identify the first term and the common difference, then use the formula a_n = a_1 + (n - 1)d.

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What is the explicit formula for the sequence -3, -33, -63, -93?

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The explicit formula is a_n = -3 - 30(n - 1).

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How do you find the 22nd term of the sequence 5, 8, 11, ...?

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Use the explicit formula: a_n = 5 + (n - 1)3. For n=22, a_22 = 68.