College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 39


$S_{1}=1$ $S_{2}=4$ $S_{3}=9$ $S_{4}=16$ $S_{5}=25$ $S_{6}=36$

Work Step by Step

We are given: $1, 3, 5, 7$ ... We notice that the terms go up by $2$. We find the pattern: $a_1=1+2(1-1)=1$ $a_2=1+2(2-1)=3$ $a_3=1+2(3-1)=5$ $a_4=1+2(4-1)=7$ Therefore: $a_n=1+2(n-1)$ $a_{n}=2n-1$ So: $a_5=1+2(5-1)=9$ $a_6=1+2(6-1)=11$ We find the partial sums: $S_{1}=1$ $S_{2}=1+3=4$ $S_{3}=1+3+5=9$ $S_{4}=1+3+5+7=16$ $S_{5}=1+3+5+7+9=25$ $S_{6}=1+3+5+7+9+11=36$
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