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: 41


$d=1.5$ $a_{n}=23.5+1.5n$ $ a_{5}=31;$ $a_{100}=173.5$

Work Step by Step

$d=a_{n+1}-a_{n}=26.5-25=28-26.5=29.5-28=1.5$ $a_{n}=a+\left( n-1\right) d\Rightarrow a_{1}=a+\left( 1-1\right) d=a=25$ $a_{n}=a+\left( n-1\right) d=25+\left( n-1\right) \times 1.5=25+1.5n-1.5=23.5+1.5n$ $a_{n}=23.5+1.5n\Rightarrow a_{5}=23.5+1.5\times 5=31;a_{100}=23.5+1.5\times 100=173.5$
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