Answer
The answer is $-2700$.
Work Step by Step
For the first series ${a_n}=-5,10,-20,40,...$.
Common ratio $r=-2$.
This is the geometric series.
Sum of the first $11$ terms.
$S_{11}=\frac{-5(1-(-2)^{11})}{1-(-2)}$.
Simplify.
$S_{11}=-3415$.
And the second series is ${b_n=10,-5,-20,-35,...}$.
Common difference $d=-15$.
The tenth terms is.
$T_{11}=10+(11-1)(-15)$
Simplify.
$T_{11}=10+10(-15)$
$T_{11}=10-150$
$T_{11}=-140$
The sum of the first $11$ terms is
$S_{11}=\frac{11}{2}\cdot (10-140)$
$S_{11}=\frac{11}{2}\cdot (-130)$
$S_{11}=11\cdot (-65)$
$S_{11}=-715$
The difference is $=-3415-(-715)$
$=-2700$.
