Answer:
2916
Explanation:
You want the 7th term of the geometric sequence that starts 4, -12, 36, -108, ...
Common ratio
The ratio of successive terms is ...
r = -12/4 = 36/-12 = -3
Seventh term
You can continue to multiply terms by -3 to find the 7th term:
a5 = -108(-3) = 324
a6 = 324(-3) = -972
a7 = -972(-3) = 2916
General term
As you know, the formula for the general term of a geometric sequence is ...
an = a1 · r^(n-1) . . . . . . where a1 is the first term
Then the 7th term is ...
a7 = 4 · (-3)^(7-1) = 4(-3)^6 = 4(729)
a7 = 2916