Algebra - Sequences Flashcards

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.

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.