Final answer:
To calculate the sum of the first 11 terms of the geometric sequence {2, 4, 8, ..., 2048}, the formula for the sum of a geometric series is used, yielding a result of 4094.
Step-by-step explanation:
Sum of the First 11 Terms of a Geometric Sequence
To find the sum of the first 11 terms of the geometric sequence {2, 4, 8, 16, 32, ...}, we use the formula for the sum of a geometric series which is Sn = a(1 - rn) / (1 - r), where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
For this sequence, a = 2 and the common ratio r = 2 since each term is twice the previous term. Plugging in these values and the number of terms, n = 11, we get:
S11 = 2(1 - 211) / (1 - 2)
Calculating the above expression:
S11 = 2(1 - 2048) / (-1)
Therefore, the sum of the first 11 terms is S11 = 4094.