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: 71

Answer

$d=22, a_1=-100.5$

Work Step by Step

With $a_4=-34.5$, the value of $a_5$ can be found by adding the common difference $d$ once. Since $a_4=-34.5$ and $a_5=-12.5$, then: \begin{align*} a_4+d&=a_5\\ -34.5+d&=-12.5\\ d&=-12.5+34.5\\ d&=22 \end{align*} To find $a_1$, use the formula $a_n=a_1+d(n-1)$ to obtain: \begin{align*} a_5&=a_1+22(5-1)\\ -12.5&=a_1+22(4)\\ -12.5&=a_1+88\\ -12.5-88&=a_1\\ -100.5&=a_1 \end{align*}
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