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Applications
- Musical sequences → chord progression
- Programming → iteration
- Finance → interest
Concepts
- Similar yet different to sets
Order Matters
- Ordered, unlike sets
Finite vs Infinite Sequences
- Finite → days of the week, alphabet
- Infinite → natural numbers
Index Notation
- Sequences start at a certain indexes depending on the context
- or
Examples
Explicit vs Recursive
- Recursive → using previous values of the sequence
- Explicit →
- Recursive →
Examples
- Given and , find
- Given and , find
Arithmetic vs Geometric
Arithmetic
- Linear, constant difference →
- General form →
Geometric
- Quadratic, constant ratio →
- General form →
Summation
- Denoted with
- → index
- → start value
- → end value
- → body
Example
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