Question

Please help

Determine if the given sequence is geometric. If the sequence is​ geometric, find the common ratio. −4​, −1​, 1​, −4​,...

A. The sequence is geometric. The common ratio is________. ​(Type an integer or a simplified​ fraction.)

B. The sequence is not geometric.

C. It cannot be determined whether the sequence is geometric or not

Answer 1

B

Explanation:

To determine if a sequence is geometric, the terms need to have a common ratio. This means that to get from one term to the next, you need to multiply by the same number. Here's an example geometric sequence:

1) 2, 4, 8, 16, 32...

2) 4, 6, 9...

As you can see, to get from one term to the next in both of these sequences, you need to multiply by a certain number [the common ratio]. In sequence one, this number is 2. You need to multiply a term by 2 to get to the next term. In the second sequence, this number is 3/2. To find this certain number/common ratio, you can set the terms into ratios:

9/6=3/2

6/4=3/2

This ratio between the terms we get is the common ratio. Multiplying by this number will get you to the next term.

In this case [-4, -1, 1, -4...]:

`(-4)/(1)=-4`

`(1)/(-1) =-1`

`(-1)/(-4)=(1)/(4)`

The ratios produced by the terms clearly aren't the same here, so the sequence is not geometric.

Answer 2

answer is (c) it cannot be determined whether the circumference is the geometrical or not