Final answer:
The sum of the first 13 terms of the given geometric sequence is 16,382, calculated using the formula for the sum of a geometric series.
Step-by-step explanation:
To find the sum of the first 13 terms of the geometric sequence 2, 4, 8, 16, 32, ..., we use the formula for the sum of the first n terms of a geometric series, which is Sn = a(1 - rn)/(1 - r), where a is the first term and r is the common ratio.
In this series, the first term a is 2 and the common ratio r is also 2, since each term is twice the previous one. Substituting these values into the formula for n = 13 we get:
S13 = 2(1 - 213)/(1 - 2) = 2(1 - 8192)/(-1) = -2(-8191) = 16382.
Therefore, the sum of the first 13 terms is 16,382.