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: 44


$d=3$ $a_{n}=3n-\left( t+3\right) $ $ a_{5} =-t+12 ;$ $a_{100}=-t+297$

Work Step by Step

$d=a_{n+1}-a_{n}=\left( -t+3\right) -\left( -t\right) =-t+6-\left( -t+3\right) =3$ $a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=-t$ $a_{n}=a+\left( n-1\right) d=-t+\left( n-1\right) \times 3=-t-3+3n=3n-\left( t+3\right) $ $a_{n}=3n-\left( t+3\right) \Rightarrow a_{5}=3\times 5-\left( t+3\right) =12-t;a_{100}=3\times 100-\left( t+3\right) =-t+297$
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