we have that the arithmetic sequence have:
[tex]\begin{gathered} a_1=2 \\ a_n=a_{n-1}+5 \end{gathered}[/tex]so we can replace for n=2,3,and 4 to find the first four terms so:
for n=2
[tex]\begin{gathered} a_2=a_{2-1}+5 \\ a_2=a_1+5 \\ a_2=2+5 \\ a_2=7 \end{gathered}[/tex]for n=3
[tex]\begin{gathered} a_3=a_{3-1}+5 \\ a_3=a_2+5 \\ a_3=7+5 \\ a_3=12 \end{gathered}[/tex]and for n=4
[tex]\begin{gathered} a_4=a_{4-1}+5 \\ a_4=a_3+5 \\ a_4=12+5 \\ a_4=17 \end{gathered}[/tex]So the first four numbers are
[tex]2,7,12,17[/tex]