An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The recursive formula have the following format:
[tex]a_{n+1}=a_n+d[/tex]Where 'd' is the common difference between each term.
From the text, we know that
[tex]\begin{gathered} a_3=5 \\ a_4=8 \end{gathered}[/tex]Plugging those values in our formula, we find that the common difference between our terms is 3.
This gives us the following recursive function:
[tex]f(n+1)=f(n)+3[/tex]Evaluating the function at '5' and '6', we get the following:
[tex]\begin{gathered} f(5)=f(4)+3=8+3=11 \\ f(6)=f(5)+3=11+3=14 \end{gathered}[/tex]