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Algebra 2 Chapter 10
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Terms in this set (27)
arithmetic means
the terms between any two nonconsecutive terms of an arithmetic sequence
arithmetic sequence
a sequence in which each term after the first is found by adding a constant (the common difference d) to the previous term
arithmetic series
the indicated sum of the terms of an arithmetic sequence
common difference
the difference between the successive terms of an arithmetic sequence
common ratio
the ratio of successive terms of a geometric sequence
convergent series
an infinite series with a sum
divergent series
an infinite geometric series that does not have a sum
explicit formula
gives a sub n as a function of n, such as a sub n=3n+1
Fibonacci sequence
a sequence in which the first two terms are 1 and each of the additional terms is the sum of the previous two terms
finite sequence
a sequence containing a limited number of terms
geometric means
the terms between any two nonsuccessive terms of a geometric sequence
geometric sequence
a sequence in which each term after the first is found by multiplying the previous term by a constant, r, called the common ratio
geometric series
the sum of the terms of a geometric sequence
induction hypothesis
the assumption that a statement is true for some positive integer k, where k ≥n
infinite geometric series
a geometric series with an infinite number of terms
infinite sequence
a sequence that continues without end
infinity
without bound, or continues without end
iteration
the process of composing a function repeatedly with itself
mathematical induction
a method of proof used to prove statements about positive integers
partial sum
the sum of the first n terms of a series
Pascal's triangle
a triangular array of numbers such that the (n+1)th row is the coefficient of the terms of the expansion (x+y)ⁿ for n=0, 1, 2,...
recursive formula
each term is formulated from one or more previous terms
recursive sequence
a sequence in which each term is determined from one or more previous terms
sequence
a list of numbers in a particular order
series
the sum of the terms of a sequence
sigma notation
for any sequence a₁, a₂, a,..., the sum of the first k terms may be written
k
∑ aⁿ
n=1
which is read "the summation from n=1 to k of aⁿ."
term
each number in a sequence or series
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