Answer
$s_{14}=\dfrac{5461}{24}=227.541$
Work Step by Step
Formula to calculate the sum of the first $n$ terms of a geometric sequence is: $s_n=\dfrac{a(1-r^n)}{(1-r)}$
Here, $r=\dfrac{a_2}{a_1}=-2$
As we are given that, $n=14$
Thus, $s_{14}=\dfrac{\dfrac{-1}{24}(1-(-2)^{14})}{(1+2)}$
or, $s_{14}=\dfrac{5461}{24}=227.541$