Let [tex]s_n[/tex] denote the number of seats in the [tex]n[/tex]-th row. [tex]s_n[/tex] is arithmetic, so
[tex]s_n=s_{n-1}+d[/tex]
for some constant [tex]d[/tex].
We're told [tex]s_5=22[/tex] and [tex]s_{10}=37[/tex], so that
[tex]s_{10}=s_9+d[/tex]
[tex]s_{10}=(s_8+d)+d=s_8+2d[/tex]
[tex]s_{10}=(s_7+d)+2d=s_7+3d[/tex]
and so on up to
[tex]s_{10}=s_5+5d\implies37=22+5d\implies5d=15\implies d=3[/tex]
The pattern continues:
[tex]s_5=s_4+3[/tex]
[tex]s_5=(s_3+3)+3=s_3+2\cdot3[/tex]
and so on up to
[tex]s_5=s_1+4\cdot3\implies22=s_1+12\implies\boxed{s_1=10}[/tex]
