Question

s the sequence geometric? If so, identify the common ratio.

2, -4, -16, -36,...

(1 point)
Responses

yes; -3
yes; -3

yes; -2
yes; -2

no
no

yes; 2

Answer 1

To determine if the sequence \(2, -4, -16, -36, \ldots\) is geometric, we need to find the ratio between consecutive terms.

The common ratio \(r\) in a geometric sequence is calculated by dividing a term by the preceding term.

1. The first term is \(2\) and the second term is \(-4\):

\[
r_1 = \frac{-4}{2} = -2
\]

2. The second term is \(-4\) and the third term is \(-16\):

\[
r_2 = \frac{-16}{-4} = 4
\]

3. The third term is \(-16\) and the fourth term is \(-36\):

\[
r_3 = \frac{-36}{-16} = \frac{36}{16} = \frac{9}{4}
\]

Since the ratios between consecutive terms are not consistent (\(-2\), \(4\), and \(\frac{9}{4}\)), the sequence is **not** geometric.

Therefore, the answer is **no**.