Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Sequences and Series
Subtopic: Geometric Sequences and Series

Overview

Our studies today take us into the second of two special sequences. Sequences such as 5, 10, 20, 40, 80, ... where you multiply a fixed number to get the next terms are called geometric sequences. This particular sequence can be written in general as {5*2^n-1}. Again it is important to be able to write the first few terms given this general formula or derive it when given the sequence's terms. Geometric series are sums where the terms are geometric such as 5+10+20+40+80+....

Something to think about: Some infinite geometric series have finite sums. Under what conditions do infinite geometric series have finite sums?

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 8.3.1 Write the first few terms of a geometric sequence given the an term
• 8.3.2 Write the next few terms of a geometric sequence given the first few terms
• 8.3.3 Find a specific term or the total number of terms in a geometric sequence
• 8.3.4 Find a specific term or the total number of terms in a geometric series
• 8.3.5 Write a geometric series in summation notation
• 8.3.6 Use formulae related to geometric sequences and series (both finite and infinite series)
• 8.3.7 Use arithmetic series to convert repeating decimals to fractions
• 8.3.8 Understand a variety of applications involving geometric sequences and series

Terminology

Terms you should be able to define: geometric sequence, first term, common ratio, nth term, geometric series, geometric sequence & series formulae

Text Notes

Concentrate on the algebraic techniques, particularly finding the n-th term, number of terms, and sum. Pay attention to the differences between a finite and infinite geometric sum.