Precalculus

# Key Terms

PrecalculusKey Terms

### Key Terms

if one event can occur in $m m$ ways and a second event with no common outcomes can occur in $n n$ ways, then the first or second event can occur in $m+n m+n$ ways
annuity
an investment in which the purchaser makes a sequence of periodic, equal payments
arithmetic sequence
a sequence in which the difference between any two consecutive terms is a constant
arithmetic series
the sum of the terms in an arithmetic sequence
binomial coefficient
the number of ways to choose r objects from n objects where order does not matter; equivalent to $C(n,r), C(n,r),$ denoted $( n r ) ( n r )$
binomial expansion
the result of expanding $(x+y) n (x+y) n$ by multiplying
Binomial Theorem
a formula that can be used to expand any binomial
combination
a selection of objects in which order does not matter
common difference
the difference between any two consecutive terms in an arithmetic sequence
common ratio
the ratio between any two consecutive terms in a geometric sequence
complement of an event
the set of outcomes in the sample space that are not in the event $E E$
diverge
a series is said to diverge if the sum is not a real number
event
any subset of a sample space
experiment
an activity with an observable result
explicit formula
a formula that defines each term of a sequence in terms of its position in the sequence
finite sequence
a function whose domain consists of a finite subset of the positive integers ${1,2,…n} {1,2,…n}$ for some positive integer $n n$
Fundamental Counting Principle
if one event can occur in $m m$ ways and a second event can occur in $n n$ ways after the first event has occurred, then the two events can occur in $m×n m×n$ ways; also known as the Multiplication Principle
geometric sequence
a sequence in which the ratio of a term to a previous term is a constant
geometric series
the sum of the terms in a geometric sequence
index of summation
in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation
infinite sequence
a function whose domain is the set of positive integers
infinite series
the sum of the terms in an infinite sequence
lower limit of summation
the number used in the explicit formula to find the first term in a series
Multiplication Principle
if one event can occur in $m m$ ways and a second event can occur in $n n$ ways after the first event has occurred, then the two events can occur in $m×n m×n$ ways; also known as the Fundamental Counting Principle
mutually exclusive events
events that have no outcomes in common
n factorial
the product of all the positive integers from 1 to $n n$
nth partial sum
the sum of the first $n n$ terms of a sequence
nth term of a sequence
a formula for the general term of a sequence
outcomes
the possible results of an experiment
permutation
a selection of objects in which order matters
probability
a number from 0 to 1 indicating the likelihood of an event
probability model
a mathematical description of an experiment listing all possible outcomes and their associated probabilities
recursive formula
a formula that defines each term of a sequence using previous term(s)
sample space
the set of all possible outcomes of an experiment
sequence
a function whose domain is a subset of the positive integers
series
the sum of the terms in a sequence
summation notation
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series
term
a number in a sequence
union of two events
the event that occurs if either or both events occur
upper limit of summation
the number used in the explicit formula to find the last term in a series
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