Answer:
Step-by-step explanation:
The formula for an explicit geometric sequence is
[tex]a_n=a_1*r^{n-1[/tex] where n is the position of the number in the sequence (ours will be 9 since we are looking for the 9th term), a1 is the first term in the sequence (ours is given as 12), and r is the common ratio (ours is given as -3). Filling all of that in to get the explicit formula we need:
[tex]a_n=12*(-3)^{n-1[/tex] and solving for the 9th term:
[tex]a_9=12*(-3)^8[/tex] which gives us, simplified a bit:
[tex]a_9=12(6561)[/tex] so
a9 = 78,732
