Let’s denote the first term of the geometric sequence as “a” and the common ratio as “r”.

The sum of the first three terms can be expressed as: a + ar + ar^2 = 9

The sum from the 4th to the 6th term can be expressed as: ar^3 + ar^4 + ar^5 = -18

To solve this system of equations, we can use substitution. Rearranging the first equation, we get: a(1 + r + r^2) = 9 a = 9 / (1 + r + r^2)

Substituting this value of “a” into the second equation, we have: (9 / (1 + r + r^2))(r^3 + r^4 + r^5) = -18

Multiplying both sides by (1 + r + r^2) to eliminate the denominator, we get: 9(r^3 + r^4 + r^5) = -18(1 + r + r^2)

Expanding both sides, we have: 9r^3 + 9r^4 + 9r^5 = -18 - 18r - 18r^2

Rearranging and simplifying, we get: 9r^5 + 9r^4 + 9r^3 + 18r^2 + 18r + 18 = 0

Dividing both sides by 9, we have: r^5 + r^4 + r^3 + 2r^2 + 2r + 2 = 0

Unfortunately, this equation does not have any rational solutions. Therefore, we cannot determine the exact values of the first term and common ratio.