The sequence is:
-21,-51,-81,-111,-141:
You need to find the difference between each term:
[tex]\begin{gathered} -51-(-21)=-30 \\ -81-(-51)=-30 \\ -111-(-81)=-30 \\ -141-(-111)=-30 \end{gathered}[/tex]The difference is -30.
You use the next formula to get the pattern:
[tex]a_n=a_1+d(n-1)[/tex]Where
an: pattern
a1: first term of the sequence
d: difference
[tex]\begin{gathered} a_n=-21+(-30)(n-1) \\ a_n=-21-30(n-1) \\ a_n=-21-30n+30 \\ a_n=-30n+9 \end{gathered}[/tex]Then, the sequence follows the pattern:
[tex]a_n=-30n+9[/tex]