### Key Terms

- Addition Principle
- if one event can occur in $m$ ways and a second event with no common outcomes can occur in $n$ ways, then the first or second event can occur in $m+n$ 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 $C(n,r),$ denoted $\left(\begin{array}{c}n\\ r\end{array}\right)$

- binomial expansion
- the result of expanding ${(x+y)}^{n}$ 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 $E$

- 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 $\{1,2,\dots n\}$ for some positive integer $n$

- Fundamental Counting Principle
- if one event can occur in $m$ ways and a second event can occur in $n$ ways after the first event has occurred, then the two events can occur in $m\times n$ 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 $m$ ways and a second event can occur in $n$ ways after the first event has occurred, then the two events can occur in $m\times n$ 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 $n$

- nth partial sum
- the sum of the first $n$ 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