The 9th term of the given geometric sequence is 59049.
The geometric sequence ha the common ratio 'r'.
The nth term of the geometric sequence is,
[tex]a_n=a_1r^{n-1}[/tex]
where, a1 is the first term of the sequence
r is the common ratio
For given example,
We have been given the geometric sequence 9, -27, 81, . . .
We need to find the 9th term.
n = 9
Also, the first term (a1) = 9
First we find the common ratio for given geometric sequence.
Since -27/9 = -3 and 81/(-27) = -3,
the common ratio (r) = -3
Using the formula of the nth term of the geometric sequence,
[tex]a_9=9\times (-3)^{9-1}\\\\a_9 = 9\times (-3)^8\\\\a_9 = 59049[/tex]
Therefore, the 9th term of the given geometric sequence is 59049.
Learn more about the geometric sequence here:
https://brainly.com/question/11266123
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