Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.2 Arithmetic Sequences and Series - 11.2 Exercises - Page 1025: 44

Answer

$$\eqalign{ & {a_n} = 2n - 4 \cr & {\text{The domain is }}D:\left\{ {1,2,3,4,5} \right\} \cr & {\text{The range is }}R:\left\{ { - 2,0,2,4,6} \right\} \cr} $$

Work Step by Step

$$\eqalign{ & {\text{From the graph we can see that}} \cr & {a_1} = - 2{\text{ and }}{a_2} = 0 \cr & {\text{Find }}d \cr & d = {a_{n + 1}} - {a_n} \cr & d = 0 - \left( { - 2} \right) \cr & d = 2 \cr & \cr & {\text{The }}n{\text{th Term of an Arithmetic Sequence is given by}} \cr & {a_n} = {a_1} + \left( {n - 1} \right)d \cr & {\text{Then}} \cr & {a_n} = - 2 + \left( {n - 1} \right)\left( 2 \right) \cr & {a_n} = - 2 + 2n - 2 \cr & {a_n} = 2n - 4 \cr & {\text{The domain is }}D:\left\{ {1,2,3,4,5} \right\} \cr & {\text{The range is }}R:\left\{ { - 2,0,2,4,6} \right\} \cr} $$
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