Final answer:
The 9th term of the geometric sequence 9, -27, 81 is calculated using the formula for the nth term of a geometric sequence; it results in 59049.
Step-by-step explanation:
To find the 9th term of the geometric sequence 9, -27, 81, we need to use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio. The common ratio (r) is found by dividing the second term by the first term. For our sequence, r = (-27) / 9 = -3. Now apply the formula to find the 9th term:
a9 = 9 × (-3)(9-1)
a9 = 9 × (-3)8
a9 = 9 × 6561
a9 = 59049
Therefore, the 9th term of the geometric sequence is 59049.