Find the sum of the first 6 terms of the geometric sequence $8,2, \frac{1}{2}, \ldots$

Step 1 ：We are given a geometric sequence with the first term \(a = 8\) and the common ratio \(r = 0.25\). We are asked to find the sum of the first 6 terms.

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

Step 3 ：Substituting the given values into the formula, we get \(S_n = 8 \cdot \frac{1 - (0.25)^6}{1 - 0.25}\).

Step 4 ：Solving the above expression, we find that \(S_n = 10.6640625\).

Step 5 ：So, the sum of the first 6 terms of the geometric sequence is \(\boxed{10.6640625}\).