SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sequence
[tex]2,-8,32,-128[/tex]STEP 2: Write the formula for calculating the common ratio
[tex]common\text{ ratio\lparen r\rparen}=\frac{T_2}{T_1}=\frac{T_3}{T_2}=\frac{T_4}{T_3}[/tex]STEP 3: Find the common ratio
[tex]\begin{gathered} T_1=2,T_2=-8,T_3=32.T_4=-128 \\ By\text{ substitution,} \\ r=\frac{-8}{2}=\frac{32}{-8}=\frac{-128}{32}=-4 \end{gathered}[/tex]Hence, the common ratio of the given sequence is -4
