Points: 0 of 10 Find the sum of the first 13 terms of the geometric sequence shown below. \[ 3,12,48,192, \ldots \] The sum of the first 13 terms is $\square$.

Step 1 ：The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. In this case, the ratio is 4 (12/3 = 4, 48/12 = 4, 192/48 = 4).

Step 2 ：The sum of the first n terms of a geometric sequence can be found using the formula: \(S_n = a * (1 - r^n) / (1 - r)\) where: \(S_n\) is the sum of the first n terms, \(a\) is the first term, \(r\) is the ratio, and \(n\) is the number of terms.

Step 3 ：In this case, \(a = 3\), \(r = 4\), and \(n = 13\).

Step 4 ：Let's plug these values into the formula and calculate the sum.

Step 5 ：Final Answer: The sum of the first 13 terms is \(\boxed{67108863}\).