Arithmetic, Geometric Sequences, Explicit, Recursive Formula

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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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CCSS.HSF.BF.A.2

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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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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 is found by subtracting any term from the subsequent term in the sequence.

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CCSS.HSF.BF.A.2

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How do you find the common ratio in a geometric sequence?

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The common ratio is found by dividing any term by the previous term in the sequence.

Tags

CCSS.HSF.BF.A.2

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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 t_n = a + (n-1)d, where a is the first term and d is the common difference.

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CCSS.HSF.BF.A.2

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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 t_n = a * r^(n-1), where a is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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What is a recursive formula?

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A recursive formula defines each term of a sequence using the preceding term(s).

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CCSS.HSF.BF.A.2

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Write the recursive formula for the arithmetic sequence 2, 5, 8, 11...

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a_n = a_{n-1} + 3, a_1 = 2.

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CCSS.HSF.BF.A.2

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Write the recursive formula for the geometric sequence 3, 6, 12, 24...

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a_n = a_{n-1} * 2, a_1 = 3.

Tags

CCSS.HSF.BF.A.2

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What is the first term of the sequence defined by t_n = 5 + (n-1)2?

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The first term is 5.

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CCSS.HSF.BF.A.2