## Precalculus (6th Edition) Blitzer

$-2700$
We are given that the sequence $a_n$ is a geometric sequence and the sequence $b_n$ is an arithmetic sequence. Here, we have $r=-2$ and $d=-15$ The general formula to find the sum of first n term of a Geometric sequence is given as: $S_{n}=\dfrac{a_1(1-r^n)}{(1-r)}$ Thus, $S_{11}=\dfrac{(-5) \times (1-(-2)^{11})}{[1-(-2)]} \\=\dfrac{(-5) \times (1+2^{11})}{[1+2]}=-3415$ The general formula to find the sum of the first n term of an Arithmetic sequence is given as: $S'_{n}=\dfrac{n(b_1+b_n)}{2}$ and $S'_{11}=\dfrac{11(b_1+b_1+(n-1)d)}{2} \\=\dfrac{11(10+10+(11-1) (-15))}{2}=-715$ Now, $S_{110}+S'_{11}=-3415-715=-2700$