Remember that
An explicit formula directly calculates the term in the sequence that you want
in this problem we have
5,8,11,14,...
so
a1=5
a2=8
a3=11
a4=14
a2-a1=8-5=3
a3-a2=11-8=3
a4-a3=14-11=3
the common difference d=3
An explicit formula is equal to
[tex]a_n=a_1+d(n-1)[/tex]
we have
a1=5
d=3
substitute
[tex]\begin{gathered} a_n=5+3(n-1) \\ a_n=5+3n-3 \\ a_n=2+3n \end{gathered}[/tex]
the answer is
an=2+3n
