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