14, 8, -16, 32...

Arithmatic. 64, 128, 256
geometric, -64, 128, -256
geometric, -48, 64, -80***
the sequence is neither geometric nor arithmatic

81, 27, 9, 3..
aruthmatic , 0,-3,-6
geometric, 0,-3,-6
geometric, 1, 1/3, 1/9

(D)

(C)

The first is (B) if you meant -4 instead of 14.

To determine whether a sequence is arithmetic or geometric, we need to check the differences between consecutive terms.

For the first sequence, the differences between the terms are as follows:
8 - 14 = -6
-16 - 8 = -24
32 - (-16) = 48

Since the differences are not constant, the sequence is not arithmetic.

Next, we can check if the ratios between consecutive terms are the same to determine if it is geometric.

For the first sequence, the ratios between the terms are as follows:
8 ÷ 14 ≈ 0.571
-16 ÷ 8 = -2
32 ÷ -16 = -2

Since the ratios are not constant, the sequence is not geometric.

Therefore, the correct answer is that the sequence is neither geometric nor arithmetic.

Now let's analyze the second sequence:

The differences between the terms are as follows:
27 - 81 = -54
9 - 27 = -18
3 - 9 = -6

Since the differences are constant (-18), the sequence is arithmetic.

The ratios between the terms are as follows:
27 ÷ 81 ≈ 0.333
9 ÷ 27 ≈ 0.333
3 ÷ 9 ≈ 0.333

Since the ratios are constant (approximately 0.333), the sequence is also geometric.

However, we need to choose only one option.

The correct answer would be that the sequence is arithmetic because the differences between the terms are constant, while the ratios between the terms are not exactly constant.