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: 43


$d=s$ $a_{n}=2+\left( n-1\right) \times s$ $ a_{5}=2+4s;$ $a_{100}=2+99s$

Work Step by Step

$t=a_{n+1}-a_{n}=\left( 2+s\right) -s=\left( 2+2s\right) -\left( 2+s\right) =s$ $a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=2$ $a_{n}=a+\left( n-1\right) d=2+\left( n-1\right) \times s$ $a_{n}=2+\left( n-1\right) \times s\Rightarrow a_{5}=2+\left( 5-1\right) \times s=2+4s;a_{100}=2+\left( 100-1\right) s=2+99s$
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