Advanced Algebra Chapter 1 & 2 Flashcards

Questions and Answers

What is a geometric sequence?

A sequence defined recursively

A sequence where each term is added with the same number

A sequence that forms a straight line

A sequence where each term is multiplied by the same number (correct)

What is an arithmetic sequence?

A sequence in which terms are found by adding the same number (correct)

A sequence defined by a recursive formula

A sequence that represents exponential growth

A sequence in which terms are found by multiplying the previous term

What is a recursive definition?

A definition that defines terms in terms of previous terms.

What does an exponential graph look like?

A J-shaped curve Signup and view all the answers

What does a linear graph represent?

A straight line Signup and view all the answers

What is the growth factor and rate of change?

Multiplication and Addition Signup and view all the answers

Provide a recursive example for a geometric sequence.

Example sequence: 2, 6, 18, 54; A(1)=2, A(n)=A(n-1)x3 for n≥2 Signup and view all the answers

Provide an nth term example for a geometric sequence.

Example sequence: 160, 40, 10, 2.5; A(n)=160(1/4^n) for n≥0 Signup and view all the answers

Provide a recursive example for an arithmetic sequence.

Example sequence: 2, 7, 12, 17; A(1)=2, A(n)=A(n-1)+5 for n≥2 Signup and view all the answers

Provide an nth term example for an arithmetic sequence.

Example sequence: 9, 5, 1, -3; A(n)=9-4n for n≥0 Signup and view all the answers

What is the volume of an open-top box?

V(x)=(l-2x)(w-2x)(x) Signup and view all the answers

What is the domain for an open-top box?

0 Signup and view all the answers

Study Notes

Geometric Sequence

Each term is generated by multiplying the previous term by a constant factor.
Important in various fields like finance and biology for modeling exponential growth.

Arithmetic Sequence

Each term is formed by adding a constant to the previous term.
Commonly used in daily life scenarios, such as calculating total costs or time increments.

Recursive Definition

A method for defining sequences where each term is based on preceding terms.
Useful in programming and mathematical concepts for defining functions.

Exponential Graph

Characterized by a J-shaped curve, indicating rapid growth.
Commonly found in real-world situations such as population growth and investment returns.

Linear Graph

Represents a straight line, indicating a constant rate of change.
Used to model relationships with linear behavior, such as distance over time.

Growth Factor and Rate of Change

Growth Factor: Involves multiplication, indicating the scale of growth.
Rate of Change: Involves addition, showing the linear increment in values.

Recursive Example (Geometric)

A specific sequence given as: 2, 6, 18, 54.
Defined recursively as A(1)=2 and A(n)=A(n-1)x3 for n≥2, illustrating exponential growth.

nth Term Example (Geometric)

Example sequence provided: 160, 40, 10, 2.5.
nth term defined as A(n)=160(1/4^n) for n≥0, demonstrating the decrease in values.

Recursive Example (Arithmetic)

Sequence shown: 2, 7, 12, 17.
Defined as A(1)=2 and A(n)=A(n-1)+5 for n≥2, representing a linear increment.

nth Term Example (Arithmetic)

Example sequence given: 9, 5, 1, -3.
nth term formula: A(n)=9-4n for n≥0, indicating a consistent negative trend.

Volume of an Open-Top Box

Volume formula is V(x)=(l-2x)(w-2x)(x), where length and width are adjusted by side cuts.
Important in optimization problems in geometry, particularly in design and manufacturing.

Domain for an Open-Top Box

Defined as 0, indicating the minimum value for dimensions within the context of the volume formula.
Highlights the practical constraint in real-world applications when constructing objects.

Description

Test your knowledge of key terms in Advanced Algebra with these flashcards covering Chapters 1 and 2. Learn about geometric sequences, arithmetic sequences, and more through concise definitions and examples.