Let the given sequence is -10,-3,4,11
The objective is to write recursive rule for the sequence.
In the given sequence each number has an equal difference between them
[tex]\begin{gathered} -3-(-10)=7 \\ 4-(-3)=7 \\ 11-4=7 \end{gathered}[/tex]So, consider the terms as,
[tex]\begin{gathered} a_1=-10 \\ a_2=-3 \\ a_2=a_1+7 \\ a_3=a_2+7 \\ a_4=a_3+7 \end{gathered}[/tex]Hence the recursive series is
[tex]a_n=a_{n-1}+d[/tex]