Answer:
A. -2.7, -9, -30, -100...
; B. -1, 2.5, -6.25, 15.625...
; D. 8, 0.8, 0.08, 0.008...
Step-by-step explanation:
A geometric sequence is one in which each term is found by multiplying each term by a constant, called the common ratio.
In sequence A, we can see that we do not add the same amount each time to find the next term; there is more difference between -2.7 and -9 than between -9 and -30.
Dividing, we find that -9/(-2.7) = 3.333333 = 3 1/3. This means that we multiply -2.7 by 3 1/3 to get 3. If we then multiply -9 by 3 1/3, we get
-9/1 * 3 1/3 = -9/1 * 10/3 = -90/3 = -30. Multiplying -30 by 3 1/3, we get
-30 * 3 1/3 = -30/1 * 10/3 = -300/3 = -100. This means A is geometric.
In sequence B, we see that multiplying -1 by -2.5 gives us 2.5. Multiplying 2.5 by -2.5 gives us -6.25; then multiplying -6.25 by -2.5 gives us 15.625. This means B is geometric.
In sequence C, we see that we would add 0.1 to each term to find the next. This is not geometric.
In sequence D, we see that multiplying 8 by 0.1 gives us 0.8. Multiplying 0.8 by 0.1 gives us 0.08; then multiplying 0.08 by 0.1 gives us 0.008. This is geometric.
In sequence D, we would multiply 4 by -1 to make -4; but then we would multiply -4 by 3 to make -12. This is not geometric.
