# Chapter 7 - Exponents and Exponential Functions - 7-8 Geometric Sequences - Practice and Problem-Solving Exercises - Page 470: 33

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 $a_{n}$=$a_{n-1}$ $\times$ $\frac{2}{3}$.

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