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which sequences are geometric? select three options.
a. -2.7, -9, -30, -
b. -1, 2.5, -6.25, 15.
c. 9.1, 9.2, 9.3, 9.
d. 8, 0.8, 0.08, 0.
e. 4, -4, -12, -

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.

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y