[tex]a_1[/tex] is the first term of the sequence, which is [tex]\boxed{-4}.[/tex]
[tex]r[/tex] is the common ratio of the sequence, the number that you multiply one term by to generate the next term. Here, we see that multiplying by -2 will generate the next term, so [tex]\boxed{r=-2}.[/tex]
We use the formula [tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex] to find the sum of the first 6 terms - just plug in our values for [tex]a_1[/tex] and [tex]r:[/tex]
[tex]S_6=\frac{-4((-2)^6-1)}{-3}=\frac{-4(63)}{-3}=\boxed{84}.[/tex]
