Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 9 - Sequences and Series - 9-2 Arithmetic Sequences - Practice and Problem-Solving Exercises - Page 577: 70


$a_1=-\dfrac{85}{4}$ $d=\frac{17}{4}$

Work Step by Step

With $a_{10}=17$, the value of $a_{14}$ can be found by adding the common difference $d$ four times. Since $a_{10}=17$ and $a_{14}=34$, then \begin{align*} a_{14}&=a_{10}+4d\\\\ 34&=17+4d\\\\ 34-17&=4d\\\\ 17&=4d\\\\ \frac{17}{4}&=\frac{4d}{4}\\\\ \frac{17}{4}&=d \end{align*} The value of $a_1$ can be found by subtracting $d$ from $a_{10}$ nine times. Thus, \begin{align*} a_1&=a_{10}-9d\\\\ a_1&=17-9\left(\frac{17}{4}\right)\\\\ a_1&=17-\frac{153}{4}\\\\ a_1&=\frac{68}{4}-\frac{153}{4}\\\\ a_1&=-\frac{85}{4} \end{align*}
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