gustavo and yuki were asked to find an explicit formula for the sequence 19, 0, -19, -38...

Answer:
Step-by-step explanation:
It's an arithmetic sequence.
[tex]0-19=-19\\-19-0=-19\\-38-(-19)=-38+19=-19[/tex]
The difference is constant.
The explicit formula of an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
Substitute:
[tex]a_1=19,\ d=-19[/tex]
[tex]a_n=19+(n-1)(-19)[/tex] use distributive property
[tex]a_n=19-19n+19\\\\a_n=(19+19)-19n\\\\a_n=38-19n[/tex]