Final answer:
The question requires finding the sum of a geometric series. The sum formula for a geometric series is applied after calculating the number of terms. By substituting the first term, common ratio, and number of terms into the formula, we get the final sum.
Step-by-step explanation:
The question asks to find the sum of the terms of the geometric sequence 1, 1.1, 1.21, ..., 1.771561. This sequence can be identified as a geometric progression where each term is multiplied by the common ratio of 1.1. The sum of a geometric series is given by the formula S = a(1 - r^n) / (1 - r), where 'a' is the first term, 'r' is the common ratio, and 'n' is the total number of terms.
To apply this formula, we need to find the number of terms 'n'. We do this by noticing that each term is formed by multiplying the previous term by 1.1. We can set up the following relation: 1.771561 = 1 * 1.1^(n-1). By solving for 'n', we get n = 17.
Now, we use the formula with a = 1, r = 1.1, and n = 17 to find the sum of the series. Plugging in the values, we get S = 1 * (1 - 1.1^17) / (1 - 1.1). After calculating, we obtain the correct sum, which corresponds to one of the multiple-choice options provided in the question.