Final answer:
To find the first term of a geometric sequence with given 4th and 7th terms, we used the formula for the nth term of a geometric sequence, found the common ratio, and solved for the first term. However, the calculated first term did not match any of the provided options, indicating a potential error in the question or the answer choices.
Step-by-step explanation:
To find the first term of a geometric sequence, we need to use the properties of geometric sequences. The nth term of a geometric sequence can be found using the formula an = a1rn-1, where an is the nth term, a1 is the first term, and r is the common ratio.
Given the 4th term (a4 = 18) and the 7th term (a7 = 2/3), we have two equations:
a1r3 = 18
a1r6 = 2/3
Dividing the second equation by the first, we eliminate a1, getting:
r3 = (2/3) / 18 = 1/27
So, r = (1/27)1/3 = 1/3.
Substituting r back into the first equation:
a1(1/3)3 = 18
a1 = 18 / (1/27) = 18 × 27 = 486
However, this is not one of the provided options, so there may have been an error in the question or the answer choices. Without an accurate answer choice, we cannot determine the correct answer matching the provided options.