Given the geometric sequence:
[tex]\frac{20}{63},-\frac{10}{21},\frac{5}{7},\ldots,\ldots,\ldots[/tex]We need to find the next three terms of the geometric sequence
So, first, we will find the common ratio of the terms as follows
The common ratio = r =
[tex]-\frac{10}{21}\div\frac{20}{63}=-\frac{10}{21}\times\frac{63}{20}=-\frac{10}{20}\times\frac{63}{21}=-\frac{1}{2}\times3=-\frac{3}{2}[/tex]So, the common ratio = r = -3/2
The next three terms will be:
[tex]\begin{gathered} -\frac{3}{2}\times\frac{5}{7}=-\frac{15}{14} \\ \\ -\frac{3}{2}\times-\frac{15}{14}=\frac{45}{28} \\ \\ -\frac{3}{2}\times\frac{45}{28}=-\frac{135}{56} \end{gathered}[/tex]So, the answer will be the terms are:
[tex]-\frac{15}{14},\frac{45}{28},-\frac{135}{56}[/tex]