# Ch 47: PLACE Mathematics: Sequences & Series

### About This Chapter

## PLACE Mathematics: Sequences and Series - Chapter Summary

Use the lessons in this chapter to study sequences and series as part of your preparation for the PLACE Mathematics exam. Our videos cover the following topics:

- Finite and infinite sequences
- Arithmetic sequences and series
- Sum of the first n terms in a sequence
- Geometric sequences
- Infinite geometric series formula
- Recursive rules for arithmetic, algebraic and geometric sequences
- Fibonacci sequence

Our knowledgeable instructors walk you through all the important concepts related to sequences and series, highlighting the most important aspects, so that you are prepared for the test. Our lessons are informative and engaging.

## Objectives of the PLACE Mathematics: Sequences and Series Chapter

The PLACE Mathematics test is a comprehensive, multiple-choice examination of your knowledge of mathematics including foundations of mathematics, functions and relations, measurement and geometry, probability and statistics, and calculus and discrete mathematics. The topics in this Sequences and Series chapter are part of the Calculus and Discrete Mathematics section of the test this section makes up 19% of the test questions. By taking the self-assessment quizzes, you can gauge your mastery of the material and obtain experience with questions similar to those used on the actual exam.

### 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. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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!

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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 PLACE Mathematics: Practice & Study Guide course

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