Answer
$a_1=1
,a_2=3
,a_3=4
,a_4=7$
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=1
\\\\
a_2=3
\\\\
a_n=a_{n-1}+a_{n-2},
\text{ if }n\ge3
,\end{array}
use the given value for $a_1.$ Then use substitution to get the next $3$ terms.
$\bf{\text{Solution Details:}}$
Using the values of $a_1,a_2,$ and $n=3,$ the third term is
\begin{array}{l}\require{cancel}
a_3=a_{3-1}+a_{3-2}
\\\\
a_3=a_{2}+a_{1}
\\\\
a_3=3+1
\\\\
a_3=4
.\end{array}
Using the values of $a_2,a_3$ and $n=4,$ the fourth term is
\begin{array}{l}\require{cancel}
a_4=a_{4-1}+a_{4-2}
\\\\
a_4=a_{3}+a_{2}
\\\\
a_4=4+3
\\\\
a_4=7
.\end{array}
Hence, the first four terms are $
a_1=1
,a_2=3
,a_3=4
,a_4=7
.$
