Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 658: 27

$S_{5}=-\dfrac{33}{4}$

Using $S_{n}=\dfrac{a_1(1-r^n)}{1-r}$, the sum of the first $ 5 $ terms of the sequence $ -12,6,-3,... $ is \begin{array}{l} S_{5}=\dfrac{-12\left(1-\left( -\dfrac{1}{2} \right)^5\right)}{1-\left( -\dfrac{1}{2} \right)}\\\\ S_{5}=\dfrac{-12\left(\dfrac{33}{32}\right)}{\dfrac{3}{2}}\\\\ S_{5}=-\dfrac{33}{4} .\end{array}