## Algebra 2 Common Core

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