Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.
Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.
To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:
-18 = a1 * r^2
9216 = a1 * r^5
Dividing these two equations, we get:
-18/9216 = (a1 * r^2) / (a1 * r^5)
-18/9216 = r^-3
r = (-18/9216)^(-1/3)
Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:
r = ((-18/9216)^(-1/3))^(1/3)
r = ((-18/9216)^(1/9))
r = (9216/-18)^(1/9)
r = (-512)^(1/9)
r = (-8)^(1/9)
r = (-2)^(2/9)
r = (-2)^(2/3)
r = (1/4)^(2/3)
r = 1/2
To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:
-18 = a1 * (1/2)^2
-18 = a1/4
a1 = -72
To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:
a4 = (-72) * (1/2)^3
a4 = -9
Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.