Find the sum of the geometric sequence \(3, 6, 12, 24, \ldots\) up to the nth term.

Step 1 ：First, we identify the common ratio of the sequence. Looking at the given sequence, we can see that each term is twice the previous term, so the common ratio \(r\) is 2.

Step 2 ：The formula for the sum of the first n terms, \(S_n\), of a geometric sequence is \(S_n = \frac{a(1 - r^n)}{1 - r}\), where \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.

Step 3 ：Substituting the given values into the formula, we get \(S_n = \frac{3(1 - 2^n)}{1 - 2} = 3(2^n - 1)\).