What is the 9th term of a geometric sequence with a first term of 12 and a
common ratio of -3?

Step-by-step explanation:

The formula for an explicit geometric sequence is

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:

and solving for the 9th term:

which gives us, simplified a bit:

so

a9 = 78,732