# Ch 46: GACE Math: Sequences & Series

### About This Chapter

## GACE Math: Sequences & Series - Chapter Summary

Completing the activities of this chapter can help you improve your understanding of sequences and series in mathematics. Start by watching the videos featuring professional instructors explaining finite and infinite sequences, then learn about the general term of sequences and how to solve mathematical problems with sequences. Following this chapter, you should be prepared for questions on the Georgia Assessments for the Certification of Educators (GACE) Mathematics exam about:

- Finding common differences of finite and infinite arithmetic sequences
- Using the general term of an arithmetic and geometric sequences
- Finding the sum of the first terms of arithmetic and geometric sequences
- Arithmetic sequences in algebra
- Formulas for infinite geometric series
- The Fibonacci Sequence
- Using recursive rules for arithmetic and geometric sequences

After watching these lesson videos, complete the lesson worksheets and quizzes to fortify your mastery over geometric sequences. Use the results from the lesson quizzes to determine what topics you haven't sufficiently mastered, and then return to the lesson videos with video tags to improve your understanding of those topics. If you have any confusion about the material of this chapter be sure to ask our instructors for clarification so that you may master the material before you take the GACE Mathematics exam.

### GACE Math: Sequences & Series Objectives

Educators in the state of Georgia take the GACE Mathematics test to demonstrate their mastery over mathematics. This certification exam involves two computer-based subtests that are each composed of 45 multiple-choice questions. Test takers may take these tests in two 2.5-hour testing sessions or one 5-hour testing session, with two hours being allowed to complete each test. Of the 45 questions on the GACE Mathematics Test I, 30% are on the subarea of Discrete Mathematics and Calculus, including arithmetic and geometric sequences. The lesson videos, worksheets and quizzes of this chapter have been put together to help you improve your understanding sequences in mathematics so that you can accurately answer these questions in a timely manner.

### 1. Introduction to Sequences: Finite and Infinite

In this video lesson, we will learn about the many patterns that are possible in sequences. See how some sequences stop after a while and how some sequences never stop.

### 2. Testing for Convergence & Divergence by Comparing Series

Comparing a series that you are given to a series that you know the answer to can help you to answer questions quickly and easily. Learn how to do so for convergence and divergence testing.

### 3. Arithmetic Sequences: Definition & Finding the Common Difference

Watch this video lesson to learn the pattern that defines an arithmetic sequence. Learn how to identify arithmetic sequences as well as find the pattern easily. You will also learn the formula you can use to write any number in your sequence.

### 4. How and Why to Use the General Term of an Arithmetic Sequence

Watch this video lesson to learn the formula for the general term of an arithmetic sequence. Also learn why this formula makes working with an arithmetic sequence much easier.

### 5. The Sum of the First n Terms of an Arithmetic Sequence

In this video lesson, you will learn an easy to use formula for summing an arithmetic sequence. Watch as we use the formula in action and then get a chance to use it yourself as you follow along.

### 6. Understanding Arithmetic Series in Algebra

In this video lesson, we will learn about arithmetic series and how they work. Learn also how to find the pattern of an arithmetic sequence along with finding the sum.

### 7. Working with Geometric Sequences

In this video lesson, we'll learn how to recognize when a sequence of numbers is a geometric sequence, how to find the common ratio and how to expand a sequence to as many numbers as we want!

### 8. How and Why to Use the General Term of a Geometric Sequence

Watch this video lesson to learn the formula for the general term of a geometric sequence. You will learn how to write your own general term given a particular geometric sequence as well as the reason for doing this.

### 9. The Sum of the First n Terms of a Geometric Sequence

Watch this video lesson to learn how you can find the total of a geometric sequence up to a certain point. Learn the formula that you can use to help you find your answer.

### 10. Understand the Formula for Infinite Geometric Series

Watch this video lesson to learn how to calculate the sum of an infinite geometric series. Learn about the interesting thing that happens when your common ratio is less than one.

### 11. Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

When dealing with sequences in math, both algebraic and geometric, we come across recursive rules. Watch this video lesson to learn how recursion works and how you can use a recursive rule to get to your next number using a previous number.

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### Other Chapters

Other chapters within the GACE Mathematics (522): Practice & Study Guide course

- GACE Math: Properties of Real Numbers
- GACE Math: Fractions
- GACE Math: Decimals & Percents
- GACE Math: Ratios & Proportions
- GACE Math: Measurements & Conversions
- GACE Math: Logic
- GACE Math: Mathematical Reasoning
- GACE Math: Vector Operations
- GACE Math: Matrices & Determinants
- GACE Math: Exponents & Exponential Expressions
- GACE Math: Algebraic Expressions
- GACE Math: Linear Equations
- GACE Math: Inequalities
- GACE Math: Absolute Value Problems
- GACE Math: Quadratic Equations
- GACE Math: Polynomials
- GACE Math: Rational Expressions
- GACE Math: Radical Expressions
- GACE Math: Systems of Equations
- GACE Math: Complex Numbers
- GACE Math: Functions
- GACE Math: Piecewise Functions
- GACE Math: Exponential & Logarithmic Functions
- GACE Math: Continuity of Functions
- GACE Math: Limits
- GACE Math: Rate of Change
- GACE Math: Calculating Derivatives & Derivative Rules
- GACE Math: Graphing Derivatives
- GACE Math: Applications of Derivatives
- GACE Math: Area Under the Curve & Integrals
- GACE Math: Integration Techniques
- GACE Math: Integration Applications
- GACE Math: Introduction to Geometric Figures
- GACE Math: Properties of Triangles
- GACE Math: Triangles, Theorems & Proofs
- GACE Math: Parallel Lines & Polygons
- GACE Math: Quadrilaterals
- GACE Math: Circular Arcs & Circles
- GACE Math: Conic Sections
- GACE Math: Geometric Solids
- GACE Math: Analytical Geometry
- GACE Math: Using Trigonometric Functions
- GACE Math: Trigonometric Graphs
- GACE Math: Solving Trigonometric Equations
- GACE Math: Trigonometric Identities
- GACE Math: Graph Theory
- GACE Math: Set Theory
- GACE Math: Overview of Statistics
- GACE Math: Summarizing Data
- GACE Math: Tables & Plots
- GACE Math: Probability
- GACE Math: Discrete Probability Distributions
- GACE Math: Continuous Probability Distributions
- GACE Math: Sampling
- GACE Math: Regression & Correlation
- GACE Mathematics Flashcards