College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Chapter 8 Review - Exercises - Page 640: 25

Answer

$5$

Work Step by Step

Let's note the arithmetic sequence by $\{a_n\}$ and the common difference by $d$. We are given: $$\begin{cases} a_4=11\\ a_6=17. \end{cases}$$ We have: $$\begin{cases} a_2=a_1+d\\ a_4=a_1+3d=11\\ a_6=a_1+5d=17. \end{cases}$$ We notice that $$a_4-a_2=2d=a_6-a_4=2d.$$ Since $a_4-a_2=a_6-a_4$ we can calculate $a_2$ directly, without calculating $a_1$ and $d$: $$\begin{align*} 11-a_2&=17-11\\ 11-a_2&=6\\ a_2&=5. \end{align*}$$ So the second term is $5$.
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