ANSWER
-3,092,446
EXPLANATION
We want to find the sum of the first 10 terms of the geometric sequence given:
[tex]19,-95,475[/tex]The common ratio of the sequence is -5 and the first term is 19.
The formula for the sum of the first n terms of a geometric sequence is:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]Therefore, for the given sequence:
[tex]\begin{gathered} S=\frac{19(1-(-5)^{10})}{1-(-5)} \\ S=\frac{19(1-9765625)}{1+5}=\frac{19(-9765624)}{6} \\ S=-3092446 \end{gathered}[/tex]That is the answer.
