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: 56



Work Step by Step

$a_{n}=a+\left( n-1\right) d$ $a_{2}=a+\left( 2-1\right) d=a+d$ $a_{5}=a+\left( 5-1\right) d=a+4d$ $a_{5}-a_{2}=3d=9.5-8=1.5\Rightarrow d=0.5$ $a_{2}=a+d\Rightarrow 8=a+0.5\Rightarrow a=7.5$ $S_{n}=\dfrac {n}{2}\left( 2a+\left( n-1\right) d\right) =\dfrac {15}{2}\left( 2\times 7.5+\left( 15-1\right) \times 0.5\right) =165$
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