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: Arithmetic Sequences and Series

Overview

Our studies today take us into the first of two special sequences. Sequences such as 4, 11, 18, 25, 32, ... where you add (or subtract) a fixed number to get the next terms are called arithmetic sequences. This particular sequence can be written in general as {4+7(n-1)}={7n-3}. 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. Arithmetic series are sums where the terms are arithmetic such as 4+11+18+25+32+....

Something to think about: Do all infinite arithmetic series have a sum of infinity?

Objectives

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

• 8.2.1 Write the first few terms of an arithmetic sequence given the an term
• 8.2.2 Write the next few terms of an arithmetic sequence given the first few terms
• 8.2.3 Find a specific term or the total number of terms in an arithmetic sequence
• 8.2.4 Find a specific term or the total number of terms in an arithmetic series
• 8.2 5 Write an arithmetic series in summation notation
• 8.2.6 Use formulae related to arithmetic sequences and series
• 8.2.7 Understand a variety of applications involving arithmetic sequences and series

Terminology

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