Answer:
18
Step-by-step explanation:
It's an arithmetic sequence:
[tex]a_1=33\\\\a_2=33-3=30\\\\a_3=30-3=27\\\\a_4=27-3=24\\\\a_5=24-3=21\\\\\text{next number}\ a_6=21-3=18[/tex]
If you need calculate any term of this sequence, then you must define an explicit formula of this sequence.
The explicit formula of an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
d - common difference
We have
[tex]d=-3,\ a_1=33[/tex]
Substitute:
[tex]a_n=33+(n-1)(-3)[/tex] use the distributive property
[tex]a_n=33+(n)(-3)+(-1)(-3)\\\\a_n=33-3n+3\\\\a_n=36-3n[/tex]
Therefore, the next number is 6th number. Substitute n = 6:
[tex]a_6=36-3(6)=36-18=18[/tex]
