Question

Find the common ratio for the geometric sequence:−0.125,0.25,−0.5,1,−2,...The common ratio is Answer

Answer 1

The given geometric sequence:

`-0.125,0.25,-0.5,1,-2,...`

The formula for the nth term of a geometric sequence whose first term is 'a' and common ratio is 'r' is:

`a_n=ar^(n-1)`

where,

`\begin{gathered} n=number\text{ of terms} \\ a=first\text{ term} \end{gathered}`

Given:

`\begin{gathered} a=-0.125 \\ a_2=ar^(2-1)=ar=0.25 \\ a_3=ar^(3-1)=ar^2=-0.5 \end{gathered}`

Hence, the common ratio is

`\begin{gathered} \frac{second\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{second\text{ term}} \\ (0.25)/(-0.125)=(-0.5)/(0.25) \\ -2=-2 \end{gathered}`

Therefore, the common ratio(r) is

`-2`