Question

Does the geometric sequence converge or diverge? Explain. Thank you!

Answer 1

A

1) The first thing to do, is to find the common ratio. So let's pick some terms and divide each one by its previous one to get the common ratio:

`\begin{gathered} (2.5)/(-10)=-0.25 \\ \\ -(0.625)/(2.5)=-0.25 \end{gathered}`

2) Now, let's take the absolute value of this ratio:

`r=|-0.25|=0.25`

3) Based on that and analyzing the options, we can tell that:

`|r|<1\Rightarrow Converges`