Question

Is each of the following a geometric sequence?

A -1,3,-9, 27, ... O Yes O No
B -1, -3, 5, 7, ...O Yes O No
C -1,4,-9, 16, ... O Yes O No
D -1, 2, 4, 8, ... O Yes O No

Answer 1

Only Sequence D is a geometric sequence.

Step-by-step explanation:

For a sequence to be geometric, each term must be obtained by multiplying the previous term by a constant factor called the common ratio. Let's analyze each sequence:

1. Sequence A: -1, 3, -9, 27, ...
   To check if it is geometric, we divide each term by the previous term to see if we obtain a constant ratio. -1/3 = -1/3 = 3/(-9) = -1/3 = -1. So, this sequence is not geometric as the common ratio is not the same for all terms.
2. Sequence B: -1, -3, 5, 7, ...
   Again, let's divide each term by the previous one. -1/(-3) = 1/3 = 5/7. In this case, the ratios are not the same for all terms, so this sequence is also not geometric.
3. Sequence C: -1, 4, -9, 16, ...
   Following the same process, we get: 4/(-1) = -4, -9/4 = -2.25, and 16/(-9) = -1.777. The ratios are not constant, so this sequence is not geometric.
4. Sequence D: -1, 2, 4, 8, ...
   Dividing each term by the previous one, we have 2/(-1) = -2, 4/2 = 2, and 8/4 = 2. The ratios are the same for all terms, which makes this sequence geometric.

In summary, only Sequence D is a geometric sequence.