Unit 5 Flashcards
A blank is an ordered set of objects, like numbers, that follow a particular pattern.
sequence
Each element in a sequence is called a blank
term.
If there is a limited number of terms, this is a blank.
finite sequence
Sequences can also continue indefinitely, which is an blank.
infinite sequence
blank are used to denote that there is no last element in an infinite sentence.
Ellipses (…)
The blank of an infinite sequence is the set of positive integers.
domain
The term an
is called the
nth term, or the blank, of the sequence.
general term
Unlike sets, the terms in blank are in some type of “order”, such as increasing, decreasing, alphabetical or alternating.
sequences
An blank for a sequence allows you to find the value of any term in the sequence without determining all previous terms.
explicit formula
The nth term of the sequence can be found by raising 2
to the blank power.
nth
A blank is a function defined by multiple subsections.
a piecewise function
How to Find Explicit Formulas for a Sequence
Look for a pattern among the terms.
If the terms are fractions, look for a separate pattern among the numerators and denominators.
Look for a pattern among the signs of the terms.
Write a formula for an
in terms of n. Test the formula for n=1, n=2, and
n=3.
A blank defined sequence is one that is defined differently for different groups of n. For example, it may be defined one way for even values of n and another for odd values of n.
piecewise
An blank is a sequence {an} such that an <= an+1
for all integers n.
increasing sequence
An blank {an} is a sequence such that an < an+1
for all integers n.
strictly increasing sequence
A blank sequence {an} is a sequence such that an >= an+1
for all integers n.
decreasing
A blank is a sequence {an}such that an > an+1for all integers n.
strictly decreasing sequence
A blank is a sequence {an} that is either increasing or decreasing.
monotone sequence
A blank is a sequence that changes by a constant factor each year,
geometric sequence
The constant factor by which a geometric sequences increases or decreases is called the blank.
common ratio
A blank is one in which any term divided by the previous term is a constant. This constant is called the common ratio of the sequence. The common ratio can be found by dividing any term in the sequence by the previous term.
geometric sequence
How to Identify a Geometric Sequence
Divide each term by the previous term.
Compare the quotients. If the quotients of any two consecutive terms are the same, a common ratio exists and the sequence is geometric.
How to Write Terms in a Geometric Sequence
Multiply the initial term by the common ratio to find the next term
Repeat the process until all four terms have been identified.
Write the terms separated by commas within brackets.
The nth term of a geometric sequence is given by what explicit formula:
an = a1r^(n-1)
