Question

Find the common ratio of the geometric sequence: 6, -2,2/3,A. -3B. 1/3C. 1D. -1/3

Answer 1

To determine the common ratio of the geometric sequence:

`6,\text{ -2 , }(2)/(3)`

The common ratio can be calculated by dividing second term and first term

or third term by second term

common ratio = r

`\begin{gathered} r=(T_2)/(T_1)=(T_3)/(T_2) \\ T_1=6,T_2=-2,T_3\text{ = }(2)/(3) \end{gathered}`
`\begin{gathered} r=(T_2)/(T_1)=(T_3)/(T_2)=(-2)/(6)=(2)/((3)/(-2)) \\ r=\text{ }(-1)/(3) \end{gathered}`

Therefore the common ratio is -1/3

Hence the correct answer is Option D