Precalculus (6th Edition)

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

Chapter 11 - Further Topics in Algebra - Chapter 11 Test Prep - Review Exercises - Page 1081: 8

Answer

$$12,10,8,6,4$$

Work Step by Step

$$\eqalign{ & {\text{arithmetic;}}\,\,\,{a_2} = 10,\,\,\,d = - 2 \cr & {\text{Substituting values for }}{a_2}{\text{ and }}d{\text{ in the formula }} \cr & {a_n} = {a_1} + \left( {n - 1} \right)d \cr & {a_2} = {a_1} + \left( {2 - 1} \right)d \cr & 10 = {a_1} + \left( {2 - 1} \right)\left( { - 2} \right) \cr & {\text{Solve for }}{a_1} \cr & 10 = {a_1} - 2 \cr & {a_1} = 12 \cr & \cr & {\text{The }}n{\text{th Term of an Arithmetic Sequence is}} \cr & {a_n} = {a_1} + \left( {n - 1} \right)d \cr & {a_n} = 12 + \left( {n - 1} \right)\left( { - 2} \right) \cr & {a_n} = 12 - 2n + 2 \cr & {a_n} = - 2n + 14 \cr & \cr & {\text{Find }}{a_3},\,\,{a_4},\,\,\,{a_5} \cr & {a_3} = - 2\left( 3 \right) + 14 = 8 \cr & {a_4} = - 2\left( 4 \right) + 14 = 6 \cr & {a_5} = - 2\left( 5 \right) + 14 = 4 \cr & \cr & {\text{The terms are:}} \cr & 12,10,8,6,4 \cr} $$
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