what is the common ratio between successive terms in the sequence? 2, -4, 8, -16, 32, -64, ... -2 -6 6 2

Explanation:

Step1: Recall common - ratio formula

For a geometric sequence (a_n), the common ratio (r=\frac{a_{n + 1}}{a_n}).

Step2: Select two successive terms

Let's take the first two terms (a_1 = 2) and (a_2=-4).

Step3: Calculate the common ratio

(r=\frac{a_2}{a_1}=\frac{-4}{2}=-2). We can double - check with other terms, say (a_3 = 8) and (a_2=-4), then (r=\frac{a_3}{a_2}=\frac{8}{-4}=-2).

Answer:

A. -2