Answer
$a_1=2
,a_2=4
,a_3=12
,a_4=48$
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=n\cdot a_{n-1}
,\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=2\cdot a_{2-1}
\\\\
a_2=2\cdot a_{1}
\\\\
a_2=2\cdot 2
\\\\
a_2=4
.\end{array}
Using the value of $a_2$ and $n=3,$ the third term is
\begin{array}{l}\require{cancel}
a_3=3\cdot a_{3-1}
\\\\
a_3=3\cdot a_{2}
\\\\
a_3=3\cdot 4
\\\\
a_3=12
.\end{array}
Using the value of $a_3$ and $n=4,$ the fourth term is
\begin{array}{l}\require{cancel}
a_4=4\cdot a_{4-1}
\\\\
a_4=4\cdot a_{3}
\\\\
a_4=4\cdot 12
\\\\
a_4=48
.\end{array}
Hence, the first four terms are $
a_1=2
,a_2=4
,a_3=12
,a_4=48
.$
