Question

What is the common ratio of the geometric series −8/9+64/81−512/729+4096/6561+⋯?
I know that to get from the first term to the second term you have to square the number, but how would I write that as a ratio?

Answer 1

looks like you are multiplying by \(-\frac{8}{9}\)

Answer 2

\[-\frac{8}{9}\times x=\frac{64}{81}\iff x=\frac{64}{81}\times- \frac{9}{8}=-\frac{8}{9}\]