Question

How do I find the common ratio (r) for the geometric sequence?2,-8,32,-128

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given sequence

`2,-8,32,-128`

STEP 2: Write the formula for calculating the common ratio

`common\text{ ratio\lparen r\rparen}=(T_2)/(T_1)=(T_3)/(T_2)=(T_4)/(T_3)`

STEP 3: Find the common ratio

`\begin{gathered} T_1=2,T_2=-8,T_3=32.T_4=-128 \\ By\text{ substitution,} \\ r=(-8)/(2)=(32)/(-8)=(-128)/(32)=-4 \end{gathered}`

Hence, the common ratio of the given sequence is -4