Question

Find the fourth term of the geometric sequence 44​, −12​, 36​, ...

Answer 1

as given, we do not have a geometric series.
I suspect the user meant 4, -12, 36, ... where r=-3
so the 4th term is -108

Answer 2

To find the fourth term of the geometric sequence, we need to find the common ratio (r) first.

Given:
First term (a) = 44
Second term = -12
Third term = 36

Using the formula for the common ratio (r):
r = (Second term) / (First term)
r = -12 / 44
r = -3/11

Now, we can find the fourth term using the formula for the nth term of a geometric sequence:
Fourth term = a * r^3
Fourth term = 44 * (-3/11)^3
Fourth term = 44 * (-27/1331)
Fourth term = -1.429

Therefore, the fourth term of the geometric sequence is approximately -1.429.

Answer 3

You are correct. Thank you for pointing out the error.

In the sequence 4, -12, 36, ... where the common ratio (r) is -3, the fourth term can be found using the formula for the nth term of a geometric sequence:

Fourth term = 4 * (-3)^3
Fourth term = 4 * (-27)
Fourth term = -108

Therefore, the fourth term of the corrected geometric sequence is -108.