Final answer:
After applying the sum formula for an infinite geometric series to the given series, we obtain 81/4 as the sum in lowest terms. However, this answer does not match any of the provided options, suggesting there may be an error in the question or the options given.
Step-by-step explanation:
The question asks us to find the sum of an infinite geometric series, given as 27, -9, 3/(-1), 1/3, and so on. We can use the formula for the sum of an infinite geometric series, which is S = a / (1 - r), where a is the first term and r is the common ratio. In this series, a = 27 and r = -1/3 (since each term is -1/3 of the previous term).
Substituting these values into the formula we get:
S = 27 / (1 - (-1/3)) = 27 / (1 + 1/3) = 27 / (4/3) = 27 * (3/4) = 81/4
Now, 81/4 is the sum in lowest terms, which gives us a = 81 and b = 4, but this option is not provided in the question. It seems there is a typo in the options or in the question itself. It's important to check the original series and calculations to ensure they are correct before selecting an answer.