Given the sequence:
[tex]\frac{1}{64}x^9y^7,-\frac{5}{32}x^6y^8,\frac{25}{16}x^3y^9,\ldots\ldots..[/tex]
the common ratio is the ratio between every two adjacent terms
So, we will find the ratio between the second term and term and the first term as follows:
[tex]-\frac{5}{32}x^6y^8\div\frac{1}{64}x^9y^7[/tex]
Simplifying the division process:
[tex]=-\frac{5}{32}\cdot\frac{64}{1}\cdot\frac{x^6}{x^9}\cdot\frac{y^8}{y^7}=-10\cdot\frac{1}{x^3}\cdot y=-\frac{10y}{x^3}[/tex]
So, the common ratio =
[tex]-\frac{10y}{x^3}[/tex]
