Sequences and Summations
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sequence
a function from the a subset of the set of integers to a set S
arithmetic progression
a sequence of the form : a + 0d , a + 1d , a + 2d , ... , a + nd where initial term a and common difference d are real numbers
geometric progression
a sequence of the form : ar⁰, ar¹, ar², ... , arⁿ where initial term a and common ratio r are real numbers
recurrence relation
an equation that expresses aₙ in terms of one or more of the previous terms of the sequence a₀, a₁, ... , aₙ₋₁, for the sequence {aₙ}
fibonacci sequence
defined by initial conditions f₀ = 0 and f₁ = 1 and the recurrence relation: fₙ = fₙ₋₁ + fₙ₋₂