Answer
$-5260$
Work Step by Step
We are given that the sequence $ a_n $ is an arithmetic sequence and the sequence $ b_n $ is a geometric sequence.
Here, we have $ r=-2$ and $ d=-15$
The general formula to find the nth term of a Geometric sequence is given as: $ a_{n}=a_1r^{n-1}$
Thus, $ a_{11}=a_1r^{11-1} =(-5)(-2)^{10} =-5120$
The general formula to find the nth term of an arithmetic sequence is given as: $ a_{n}=a_1+(n-1) d $
and $ b_{11}=10+(11-1) (-15) =10-150=-140$
Now, $ a_{11}+b_{11}=-5120-140=-5260$
