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 - Page 857: 35


$d=-18$ $a_{n}=47-18n$ $ a_{5}=-43;$ $a_{100}=-1753$

Work Step by Step

$d=a_{n+1}-a_{n}=11-29=-7-11=-25-\left( -7\right) =-18$ $a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=29$ So the nth term $a_{n}=a+\left( n-1\right) d=29+\left( n-1\right) \times \left( -18\right) =29-18n+18=47-18n$ $a_{n}=47-18n\Rightarrow a_{5}=47-18\times 5=-43;a_{100}=47-18\times 100=-1753$
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