Arithmetic and Geometric Sequences Recursive and 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 common difference (d) in an arithmetic sequence?

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The common difference (d) is the fixed amount added to each term to get the next term in an arithmetic sequence.

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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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What is the common ratio (r) in a geometric sequence?

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The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

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What is the explicit formula for an arithmetic sequence?

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The explicit formula for 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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What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is a(n) = a(1) * r^(n-1), where a(1) is the first term and r is the common ratio.

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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 formula a(n) = a(1) + (n-1)d.

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How do you find the nth term of a geometric sequence?

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To find the nth term of a geometric sequence, use the formula a(n) = a(1) * r^(n-1).

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What is a recursive formula for an arithmetic sequence?

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A recursive formula for an arithmetic sequence is a(n) = a(n-1) + d, where d is the common difference.

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What is a recursive formula for a geometric sequence?

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A recursive formula for a geometric sequence is a(n) = a(n-1) * r, where r is the common ratio.