AP PreCalculus Flashcards: Change in Arithmetic and Geometric Sequences
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
How can a geometric sequence be described in terms of its change?
A geometric sequence has a constant proportional change, as successive terms have a common ratio.
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How can a geometric sequence be described in terms of its change?
A geometric sequence has a constant proportional change, as successive terms have a common ratio.
In the formula g_{n} = g_{0}r^{n}, what do the variables g_{0} and r represent?
The variable g_{0} represents the initial value of the sequence, and r represents the common ratio.
What is the general term formula for a geometric sequence?
The general term of a geometric sequence is given by the formula g_{n} = g_{0}r^{n}.
How are arithmetic sequences expressed as functions?
Arithmetic sequences are expressed as functions where the domain is the whole numbers and the output is determined by an initial value and a common difference.
In the formula a_{n} = a_{0} + dn, what do the variables a_{0} and d represent?
The variable a_{0} represents the initial value of the sequence, and d represents the common difference.
Why does the graph of a sequence consist of discrete points?
Because a sequence is a function from the whole numbers, its graph consists of discrete points rather than a continuous curve.
A contextual scenario involves a quantity being multiplied by the same factor per time period. What type of sequence function models this?
A geometric sequence models this scenario because it is defined by a common ratio, which represents a constant proportional change.
What is the common difference in an arithmetic sequence?
The common difference is the constant rate of change between successive terms in an arithmetic sequence.
What is the general term formula for an arithmetic sequence?
The general term of an arithmetic sequence is given by the formula a_{n} = a_{0} + dn.
How are geometric sequences expressed as functions?
Geometric sequences are expressed as functions where the domain is the whole numbers and the output is determined by an initial value and a common ratio.
A contextual scenario involves a quantity changing by a constant amount per time period. What type of sequence function models this?
An arithmetic sequence models this scenario because it is defined by a common difference, which represents a constant rate of change.
What is a sequence?
A sequence is a function from the whole numbers to the real numbers.
What is the common ratio in a geometric sequence?
The common ratio is the constant proportional change between successive terms in a geometric sequence.
How can an arithmetic sequence be described in terms of its rate of change?
An arithmetic sequence has a constant rate of change, as successive terms have a common difference.