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

Question

asked Feb 15, 2023 218k views

1 Answer

Hirt · Answer 1 · 2023-02-21T13:12:10+0000

SOLUTION

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

STEP 1: Write the given sequence

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