Exploring the world of sequences, this content delves into arithmetic and geometric sequences, their defining characteristics, and practical applications. Arithmetic sequences progress by a constant difference, while geometric sequences grow by a constant ratio. These mathematical patterns are not only fundamental in theory but also serve as tools for modeling phenomena such as population growth and financial planning. Understanding these sequences is crucial for analyzing progression and regression in various contexts.
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Arithmetic sequences follow a constant difference between terms, with a formula to calculate any term
Geometric sequences have a constant ratio between terms, with a formula to calculate any term
Recurrence relations define terms in a sequence through a recursive formula
Increasing sequences have each term greater than the previous one
Decreasing sequences have each term smaller than the previous one
Periodic sequences repeat their terms in a regular cycle
Sequences can be used to model situations such as population growth or financial investments
Arithmetic sequences can represent scenarios with a uniform increase by a fixed amount
Geometric sequences can describe situations with exponential growth or decay
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Definition of Arithmetic Sequence
A sequence with a constant difference between consecutive terms.
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Common Difference in Arithmetic Sequence
The fixed amount added to each term to get the next term.
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Example of Arithmetic Sequence
Sequence 2, 5, 8, 11... with a common difference of 3.
