Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 29

$8191.5$

The general formula to find the nth partial sum of a Geometric sequence is given as: $ S_{n}=\dfrac{a(1-r^n)}{(1-r)}$ $ r=\dfrac{a_2}{a_1}=\dfrac{3}{-3/2}=-2$ and $ n=14$ Now, $ S_{14}=\dfrac{\dfrac{-3}{2}(1-(-2)^{11})}{(1-(-2))}=\dfrac{-3}{2} \times \dfrac{16383}{3}$ Our answer is: $ S_{14}=8191.5$