Find the sum of the first 14 terms of the geometric sequence. Use the formula for the sum of the first $n$ terms of a geometric sequence. \[ 3,-6,12,-24, \ldots \]

Step 1 ：We are given a geometric sequence where each term is multiplied by -2 to get the next term. The first term (a) is 3 and the common ratio (r) is -2. We are asked to find the sum of the first 14 terms (n=14).

Step 2 ：The formula for the sum of the first n terms of a geometric sequence is: \[S_n = \frac{a(r^n - 1)}{r - 1}\]

Step 3 ：We can substitute the given values into this formula to find the sum. a = 3, r = -2, n = 14.

Step 4 ：Substituting these values into the formula, we get \[S_n = \frac{3((-2)^{14} - 1)}{-2 - 1} = -16383.0\]

Step 5 ：Final Answer: The sum of the first 14 terms of the geometric sequence is \(\boxed{-16383}\)