Answer: Let's denote the first term of the geometric sequence as "a", and the common ratio as "r". Then, we can use the given information to set up a system of equations:
a * r^3 = 18 (the fourth term is 18, so ar^3 is the fourth term)
a * r^6 = 16/3 (the seventh term is 16/3, so ar^6 is the seventh term)
To solve for "a" and "r", we can divide the second equation by the first equation:
(a * r^6) / (a * r^3) = (16/3) / 18
Simplifying this expression, we get:
r^3 = (16/3) / 18 = 16/54 = 8/27
Taking the cube root of both sides, we get:
r = 2/3
Substituting this value of "r" into the first equation, we can solve for "a":
a * (2/3)^3 = 18
a = 18 / (2/3)^3
a = 27
Therefore, the first term of the geometric sequence is 27, and the nth term is given by:
a * r^(n-1) = 27 * (2/3)^(n-1)
Explanation: