What is the first term of the sequence defined by the recursive formula $$u_n = u_{n-1} - 3$$ ?

The first term is defined as $$u_1 = 15$$ .

What is the recursive formula for the sequence 15, 12, 9, 6, 3?

The recursive formula is $$u_1 = 15$$ and $$u_n = u_{n-1} - 3$$ .

How do you find the 5th term of the sequence defined by $$a_n = 3 \times 2^{(n-1)}$$ ?

Substituting n=5 gives $$a_5 = 3 \times 2^{(5-1)} = 48$$ .

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

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

What does the term 'common ratio' refer to in a geometric sequence?

The common ratio is the factor by which each term is multiplied to get the next term.

What does the term 'common difference' refer to in an arithmetic sequence?

The common difference is the amount added to each term to get the next term.

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

To convert, identify the pattern in the sequence and express the nth term in terms of n.

What is the significance of the first term in a recursive formula?

The first term serves as the starting point for generating all subsequent terms in the sequence.

What is the relationship between recursive and explicit formulas?

Both formulas describe the same sequence but in different ways; recursive uses previous terms, while explicit uses the term's position.

Flashcard

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Mathematics

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9th - 12th Grade

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Practice Problem

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Hard

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CCSS

HSF.BF.A.2, HSF.IF.A.3

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FLASHCARD QUESTION

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. It specifies the first term and a rule for finding subsequent terms.

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

What is the explicit formula for an arithmetic sequence?

Back

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

What is the explicit formula for a geometric sequence?

Back

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.BF.A.2

FLASHCARD QUESTION

Front

Given the sequence 9, 5, 1, -3, what is the common difference?

Back

The common difference is -4.

Tags

CCSS.HSF.BF.A.2

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