Chapter 9
A sequence is an _________ sequence when the first differences are all the same nonzero number.
Arithmetic
A sequence is called an _________ sequence when the differences between consecutive terms are the same. This difference is called the _________ difference.
Arithmetic
To find binomial coefficients, you can use the _________ _________ or _________ _________.
Binomial Theorem or Pascal's Triangle
The coefficients of a binomial expansion are called _________ _________.
Binomial coefficients
When selecting subsets of a larger set in which order is not important, you are finding the number of __________ of n elements taken r at a time.
Combinations
The number of __________ __________ of n objects is given by n!/n1!n2!n3!.....nk!
Distinguishable permutations
When you write the coefficients for a binomial that is raised to a power, you are _________ a _________.
Expanding a binomial
An __________ is any happening for which the result is uncertain, and the possible resilts are called __________.
Experiment Outcomes
If n is a positive integer, then n _________ is defined as n! = 1 * 2 * 3 * 4 ... (n - 1) * n.
Factorial
A sequence is a _________ sequence when the domain of the function consists only of the first n positive integers.
Finite
To find the _________ differences of a sequence, subtract consecutive terms.
First
The __________ __________ __________ states that when there are m1 different ways for one event to occur and m2 different ways for a second event to occur, there are m1 * m2 ways for both events to occur.
Fundamental Counting Principle
A sequence is called a _________ sequence when the ratios of consecutive terms are the same. This ratio is called the _________ ratio.
Geometric Common
If P(E) = 0, then E is an __________ event, and if P(E) = 1, then E is a __________ event.
Impossible Certain
The __________ of an event A is the collection of all outcomes in the sample space that are not in A.
Independent
An _________ _________ is a function whose domain is the set of positive integers.
Infinite sequence
The first step in proving a formula by _________ _________ is to show that the formula is true when n = 1.
Mathematical induction
If two events from the same sample spaces have no outcomes in common, then the two events are __________ __________.
Mutually exclusive
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The sum of a finite geometric sequence with common ration, where r does not equal 1, is given by _________.
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An ordering of n elements is called a __________ of the elements.
Permutation
To determine the __________ of an event, you can use the formula P(E) = n(E)/n(S), where n(E) is the number of outcomes in the event and n(S) is the number of outcomes in sample space.
Probability
When you know the nth term of an arithmetic sequence and you know the common difference of the sequence, you can find the (n + 1)th term by using the _________ formula a sub n+1 = a sub n + d
Recursion
If you are given one or more of the first few terms of a sequence, and all other terms of the sequence are defined using previous terms, then the sequence is said to be defined _________.
Recursively
The sum of the terms of an infinite geometric sequence is called a _________ _________.
S = a1/(1 - r)
The set of all possible outcomes of an experiment is called the __________ __________.
Sample space
If the _________ differences of a sequence are all the same nonzero number, then the sequence has a perfect quadratic model.
Second
Chapter 9
Section 1
Chapter 9
Section 2
Chapter 9
Section 3
Chapter 9
Section 4
Chapter 9
Section 5
Chapter 9
Section 6
Chapter 9
Section 7
The sum of the terms of a finite or infinite sequence is called a _________.
Series
You can use the formula Sn = n/2(a1 + an) to find the sum of the first n terms of an arithmetic sequence, which is called the _________ of a _________ _________ _________.
Sum of a finite arithmetic sequence
The nth term of a geometric sequence has the form _________.
an = a1 * r raised to n - 1
The nth term of an arithmetic sequence has the form _________.
an= a1 + (n - 1)d
The number of combinations of n elements taken r at a time is given by __________.
n!/(n -r)! r!
The symbol used to denote a binomial coefficient is __________ or __________.
n/r or nCr
The number of permutations of n elements taken r at at time is given by __________.
nPr
