To find the common ratio of the geometric sequence, we can take any two consecutive terms and divide the second term by the first term.
Let's consider the first two terms of the sequence:
- The first term (a₁) is -2.
- The second term (a₂) is 4.
Now, we can find the common ratio (r):
\[ r = \frac{a_2}{a_1} = \frac{4}{-2} = -2 \]
We can also verify this with the next terms:
-
The third term (a₃) is -8. \[ r = \frac{a_3}{a_2} = \frac{-8}{4} = -2 \]
-
The fourth term (a₄) is 16. \[ r = \frac{a_4}{a_3} = \frac{16}{-8} = -2 \]
-
The fifth term (a₅) is -32. \[ r = \frac{a_5}{a_4} = \frac{-32}{16} = -2 \]
The common ratio \( r \) is consistently -2 throughout the sequence.
None of the provided answer choices directly state the common ratio as -2. However, let's evaluate the answer choices to see which one might correspond to -2 based on the calculations:
A - 4/2 = 2
B - -2/4 = -0.5
C - 2/4 = 0.5
D - 4/2 = 2
None of the options seem to represent -2, but the closest representation which correctly divides to provide -2 checkpoints isn't listed correctly among the options.
The common ratio of the sequence is -2.