Determine whether each sequence is arithmetic or geometric. Find the next three terms.

-4,8,-16,32...
A. Arithmetic, 64,128,256
B. Geometric, -64,128,-256
C. Geometric, -48,64,-80
D. The sequence is neither arithmetic nor geometric sequence.
B?
Thank you

Yes, this is correct. The common ratio is -2 times the precious term.

Thank you again sooooooooooooo much. You are a great help!:) Your really smart.

I put precious instead of previous. Oh well. Typos happen. But no problem! Glad to help!

lol I didn't even notice. Thanks.

To determine whether a sequence is arithmetic or geometric, we need to examine the pattern between the terms.

In the given sequence: -4, 8, -16, 32...

If the difference between consecutive terms is constant, then it is an arithmetic sequence.

Let's check the differences between terms:
8 - (-4) = 12
(-16) - 8 = -24
32 - (-16) = 48

As the differences are not constant, we can conclude that the sequence is not arithmetic.

Alternatively, if the ratio between consecutive terms is constant, then it is a geometric sequence.

Let's check the ratios between terms:
8 / (-4) = -2
(-16) / 8 = -2
32 / (-16) = -2

As the ratios are constant (-2), we can conclude that the sequence is geometric.

Now, to find the next three terms in a geometric sequence, we need to continue multiplying each term by the common ratio.

The common ratio for this sequence is -2.

32 * (-2) = -64
-64 * (-2) = 128
128 * (-2) = -256

Therefore, the next three terms are -64, 128, -256.

So, the correct answer is B. Geometric, -64, 128, -256.