Exercise 34 Page 319

We want to write the recursive formula for the given geometric sequence. Looking at the explicit formula, we can identify the common ratio r and the value of the first term a_1. a_n= -81 ( 2/3)^(n-1) We can see that 23 is the common ratio and the first term is -81. Now we have enough information to form an recursive formula for this sequence. \begin{gathered} la_1=a a_n=r* a_(n-1) \quad \Rightarrow \quad la_1= -81 a_n=( 2/3 )a_(n-1) \end{gathered}