Answer
$a_1=-2
,a_2=1
,a_3=4
,a_4=7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the first four terms of the given sequence
\begin{array}{l}\require{cancel}
a_1=-2
\\\\
a_n=a_{n-1}+3,
\text{ if }n\gt1
,\end{array}
use the given value for $a_1.$ Then use substitution to get the next $3$ terms.
$\bf{\text{Solution Details:}}$
Using the value of $a_1$ and $n=2,$ the second term is
\begin{array}{l}\require{cancel}
a_2=a_{2-1}+3
\\\\
a_2=a_{1}+3
\\\\
a_2=-2+3
\\\\
a_2=1
.\end{array}
Using the value of $a_2$ and $n=3,$ the third term is
\begin{array}{l}\require{cancel}
a_3=a_{3-1}+3
\\\\
a_3=a_{2}+3
\\\\
a_3=1+3
\\\\
a_3=4
.\end{array}
Using the value of $a_3$ and $n=4,$ the fourth term is
\begin{array}{l}\require{cancel}
a_4=a_{4-1}+3
\\\\
a_4=a_{3}+3
\\\\
a_4=4+3
\\\\
a_4=7
.\end{array}
Hence, the first four terms are $
a_1=-2
,a_2=1
,a_3=4
,a_4=7
.$