Questions and Answers
What is the term of a sequence?
What is a sequence?
A pattern involving an ordered arrangement of numbers, geometric figures, letters, or other objects.
What is the common difference in an arithmetic sequence?
The difference between any two successive terms.
What is an arithmetic sequence?
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What characterizes a geometric sequence?
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What is the common ratio in a geometric sequence?
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What does a recursive formula express?
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What is an explicit formula?
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What is the explicit formula for a geometric sequence?
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What is the explicit formula for an arithmetic sequence?
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What does a recursive formula for an arithmetic sequence express?
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What does a recursive formula for a geometric sequence express?
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Study Notes
Terms and Definitions
- Term of a Sequence: Individual number, figure, or letter within a sequence.
- Sequence: Ordered arrangement of numbers, figures, letters, or other objects demonstrating a specific pattern.
Types of Sequences
- Common Difference: The fixed difference between any two successive terms in an arithmetic sequence.
- Arithmetic Sequence: A sequence where each term is found by adding the same value (common difference) to the previous term; characterized by a constant difference between consecutive terms.
- Geometric Sequence: A sequence where the ratio between any two consecutive terms remains constant; defined by multiplying by the same value (common ratio) to obtain successive terms.
Common Ratios and Differences
- Common Ratio: The constant ratio between consecutive terms in a geometric sequence.
Formulas
- Recursive Formula: Provides a method to determine each term based on the preceding term; essential for understanding sequences that build on prior values.
- Explicit Formula: A direct method to calculate each term by using its position in the sequence; useful for finding the nth term without needing the previous terms.
Specific Formulas (Pending Definitions)
- Explicit Formula for a Geometric Sequence: Not detailed but would involve the initial term and the common ratio.
- Explicit Formula for an Arithmetic Sequence: Not detailed but would involve the first term and common difference.
- Recursive Formula for an Arithmetic Sequence: Not detailed but would iterate using the previous term.
- Recursive Formula for a Geometric Sequence: Not detailed but would also depend on the previous term, utilizing the common ratio.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of sequences with these flashcards focused on key terms such as 'term of a sequence', 'common difference', and 'arithmetic sequence'. Ideal for reinforcing your knowledge in algebraic concepts and sequence patterns.
