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A detailed guide to arithmetic sequences (also known as arithmetic progressions), including how to identify them, how to find the terms, creating formulae to describe the terms of an arithmetic sequences, calculating the sum and mean of an sequence, and more. Easy-to-follow step-by-step explanations, numerous examples, and 80 questions and answers - including showing you to solve each question and reach the answer.
INTRODUCING ARITHMETIC SEQUENCES
What is a Sequence?
What is an Arithmetic Sequence?
Checking if a Sequence is an Arithmetic Sequence
Finding the Common Difference of an Arithmetic Sequence from Adjacent Terms
Finding the Common Difference of an Arithmetic Sequence from Non-Adjacent Terms
Finding the Next Terms in an Arithmetic Sequence
Finding the Previous Terms in an Arithmetic Sequence
Finding Missing Terms in an Arithmetic Sequence
FINDING AND USING THE FORMULA FOR A PARTICULAR ARITHMETIC SEQUENCE
Finding the Formula
Using the Formula to Find a Particular Term
Using the Formula to Check Whether and Where a Particular Term is in a Sequence
Using the Formula to Find the First Term Greater Than a Target Value
Using the Formula to Find the First Term Less Than a Target Value
A GENERAL FORMULA FOR THE TERMS IN AN ARITHMETIC SEQUENCE
Creating the Formula
Using the Formula
Finding the Values of a and d
CALCULATING THE SUM AND MEAN OF AN ARITHMETIC SEQUENCE
Gauss at Elementary School
Generating a Formula for the Sum of Arithmetic Sequence
Using the Sum Formula
Finding the Sum of Ranges of Terms within an Arithmetic Sequence
Generating a Formula for the Arithmetic Mean of an Arithmetic Sequence
Simultaneous Equations Involving the Sum and/or Mean.