As per given by the question,
There are given the sequence, -5, -8, -11, and -14.
Now,
For find the recursive formula,
There is need to know about the common difference.
Then,
From the given sequence, the common difference is;
[tex]\begin{gathered} -8-(-5)=-8+5 \\ =-3 \end{gathered}[/tex]So,
here, d=-3.
Now,
The recursive formula is,
[tex]a_n=a(n-1)-3[/tex]He