$\begin{array} { l }r=\frac{ -\frac{ 32 }{ 3 } }{ 8 },\\r=\frac{ \frac{ 128 }{ 9 } }{ -\frac{ 32 }{ 3 } },\\r=\frac{ -\frac{ 512 }{ 27 } }{ \frac{ 128 }{ 9 } }\end{array}$
Simplify the expression$\begin{array} { l }r=-\frac{ 4 }{ 3 },\\r=\frac{ \frac{ 128 }{ 9 } }{ -\frac{ 32 }{ 3 } },\\r=\frac{ -\frac{ 512 }{ 27 } }{ \frac{ 128 }{ 9 } }\end{array}$
Simplify the expression$\begin{array} { l }r=-\frac{ 4 }{ 3 },\\r=-\frac{ 4 }{ 3 },\\r=\frac{ -\frac{ 512 }{ 27 } }{ \frac{ 128 }{ 9 } }\end{array}$
Simplify the expression$\begin{array} { l }r=-\frac{ 4 }{ 3 },\\r=-\frac{ 4 }{ 3 },\\r=-\frac{ 4 }{ 3 }\end{array}$
Since the ratio between each pair of consecutive terms is the same, the sequence is geometric and the common ratio is $r=-\frac{ 4 }{ 3 }$$r=-\frac{ 4 }{ 3 }$
To find the next term, multiply the last term $-\frac{ 512 }{ 27 }$ by the common ratio $r=-\frac{ 4 }{ 3 }$$-\frac{ 512 }{ 27 } \times \left( -\frac{ 4 }{ 3 } \right)$
Calculate the product$\frac{ 2048 }{ 81 }$
To find the next term, multiply the last term $\frac{ 2048 }{ 81 }$ by the common ratio $r=-\frac{ 4 }{ 3 }$$\frac{ 2048 }{ 81 } \times \left( -\frac{ 4 }{ 3 } \right)$
Calculate the product$-\frac{ 8192 }{ 243 }$
To find the next term, multiply the last term $-\frac{ 8192 }{ 243 }$ by the common ratio $r=-\frac{ 4 }{ 3 }$$-\frac{ 8192 }{ 243 } \times \left( -\frac{ 4 }{ 3 } \right)$
Calculate the product$\frac{ 32768 }{ 729 }$
To find the next term, multiply the last term $\frac{ 32768 }{ 729 }$ by the common ratio $r=-\frac{ 4 }{ 3 }$$\frac{ 32768 }{ 729 } \times \left( -\frac{ 4 }{ 3 } \right)$
Calculate the product$-\frac{ 131072 }{ 2187 }$
The next four terms are $\begin{array} { l }\frac{ 2048 }{ 81 },& -\frac{ 8192 }{ 243 },& \frac{ 32768 }{ 729 },& -\frac{ 131072 }{ 2187 }\end{array}$$\begin{array} { l }\frac{ 2048 }{ 81 },& -\frac{ 8192 }{ 243 },& \frac{ 32768 }{ 729 },& -\frac{ 131072 }{ 2187 }\end{array}$