Answer
$227.54$
Work Step by Step
First, we must determine the common ratio between the terms:
$r=\frac{\frac{1}{12}}{-\frac{1}{24}}=\frac{\frac{-1}{6}}{\frac{1}{12}}=\frac{\frac{1}{3}}{-\frac{1}{6}}=-2$
For solving this, we will use the formula of the finite geometric series. $S_{n}=\frac{a_{1}\times (1-r^{n})}{1-r}$. Then put correct value for $7th$ term to solve.
$S_{14}=\frac{(-\frac{1}{24}) \times (1-(-2)^{14})}{1-(-2)}=227.54$