Answer
$10+\sqrt{7}, 10, 10-\sqrt{7}, 10-2\sqrt{7}, 10-3\sqrt{7}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the first $5$ terms, solve first the common difference. Then keep adding the common difference to the given second term.
$\bf{\text{Solution Details:}}$
The common difference is the difference between a term and the term before it. Hence, the common difference, $d,$ is
\begin{array}{l}\require{cancel}
d=a_2-a_1
\\\\
d=10-(10+\sqrt{7})
\\\\
d=10-10-\sqrt{7}
\\\\
d=-\sqrt{7}
,\end{array}
Adding the common difference, the third term is
\begin{array}{l}\require{cancel}
a_3=a_2+d
\\\\
a_3=10-\sqrt{7}
,\end{array}
the fourth term is
\begin{array}{l}\require{cancel}
a_4=a_3+d
\\\\
a_4=10-\sqrt{7}-\sqrt{7}
\\\\
a_4=10-2\sqrt{7}
,\end{array}
and the fifth term is
\begin{array}{l}\require{cancel}
a_5=a_4+d
\\\\
a_5=10-2\sqrt{7}-\sqrt{7}
\\\\
a_5=10-3\sqrt{7}
,\end{array}
Hence, the first $5$ terms are $
10+\sqrt{7}, 10, 10-\sqrt{7}, 10-2\sqrt{7}, 10-3\sqrt{7}
.$
