Answer
The recursive formula is $a_{1}$=192 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{2}{3}$.
Work Step by Step
Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r.
The starting value is 192 so it is the $a_{1}$
You have the sequence 192,128,64 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{128}{192}$=$\frac{2}{3}$ and r=$\frac{64}{128}$=$\frac{2}{3}$.So the common ratio is $\frac{2}{3}$.Substitute the value of a1 and R into the recursive formula:
The recursive formula is $a_{1}$=192 and $a_{n}$=$a_{n-1}$ $\times$ $\frac{2}{3}$.
