Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.2 - Arithmetic Sequences - 12.2 Exercises: 48

Answer

$a_{1}=195$ $a_{n}=195-7n+7=202-7n$

Work Step by Step

$a_{n}=a+\left( n-1\right) d;a_{m}=a+\left( m-1\right) d\Rightarrow a_{n}-a_{m}=\left( n-m\right) d$ $a_{12}-a_{8}=\left( 12-8\right) \times d=118-146=-28\Rightarrow d=-7$ $a_{8}-a_{1}=\left( 8-1\right) \times d\Rightarrow 146-a_{1}=7\times \left( -7\right) \Rightarrow a_{1}=195$ $a_{n}-a_{1}=\left( n-1\right) d\Rightarrow a_{n}-195=\left( n-1\right) \times \left( -7\right) \Rightarrow a_{n}=195-7n+7=202-7n$
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