Question

What is the 9th term of a geometric

sequence with a first term of 12 and a
common ratio of -3?

Answer 1

Explanation:

The formula for an explicit geometric sequence is

`a_n=a_1*r^{n-1` 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:

`a_n=12*(-3)^{n-1` and solving for the 9th term:

`a_9=12*(-3)^8` which gives us, simplified a bit:

`a_9=12(6561)` so

a9 = 78,732