Recursive Sequences

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What is a recursive sequence?

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A recursive sequence is a sequence of numbers where each term is defined as a function of one or more of the preceding terms.

Front

What is the formula for a geometric recursive sequence?

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What is the formula for an arithmetic recursive sequence?

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Front

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

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To find the nth term, you start from the initial term and apply the recursive formula repeatedly until you reach the nth term.

Front

What is the rebound height of a ball dropped from 20 meters with a rebound ratio of 0.8?

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The heights form the sequence: {20, 16, 12.8, 10.24, ...}.

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Front

What is the rebound height of a ball dropped from 15 meters with a rebound ratio of 0.6?

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The height will be 9 meters.

Front

What is the recursive formula for the sequence 1, 2, 5, 14, 41, 122, ...?

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Front

How do you convert a recursive formula to an explicit formula?

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You analyze the pattern of the sequence and derive a formula that directly calculates the nth term without recursion.

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The first term is 22.