Answer :
By definition, in a Geometric sequence the terms are found by multiplying the previous one by a constant. This constant is called "Common ratio".
In this case, you know these values of the set:
[tex]\begin{gathered} .004 \\ .4 \end{gathered}[/tex]Notice that you can set up this set with the value given in the first option:
[tex].004,.04,.4[/tex]Now you can check it there is a Common ratio:
[tex]\begin{gathered} \frac{0.04}{0.004}=10 \\ \\ \frac{.4}{0.04}=10 \end{gathered}[/tex]The Common ratio is:
[tex]r=10[/tex]Therefore, it is a Geometric sequence.
Apply the same procedure with each option given in the exercise:
- Using
[tex].004,.04,-.04,.4[/tex]You can notice that it is not a Geometric sequence, because:
[tex]\begin{gathered} \frac{-.04}{.04}=-1 \\ \\ \frac{.4}{-.04}=-10 \end{gathered}[/tex]- Using
[tex].004,.0004,.4[/tex][tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{4}{.0004}=1,000 \end{gathered}[/tex]Since there is no Common ratio, if you use the value given in the third option, you don't get a Geometric sequence.
- Using this set with the values given in the last option:
[tex].004,.0004,-.0004,.4[/tex]You get:
[tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{-.0004}{.0004}=-1 \end{gathered}[/tex]It is not a Geometric sequence.
The answer is: First option.
