Exercise 29 Page 319

The explicit formula of a geometric sequence combines the information provided by the two equations of the recursive form into a single equation. Recursive:& a_1= a_1; a_n= r* a_(n-1) Explicit:& a_n= a_1 r^(n-1)In these formulas, r is the common ratio and a_1 is the first term. Looking at the given explicit formula, we can identify the common ratio r and the value of the first term a_1. a_n= 7( 3)^(n-1) We can see that 3 is the common ratio and the first term is 7. Now we have enough information to form a recursive formula for this sequence. \begin{gathered} la_1 = a_1 a_n = r* a_(n-1) \quad \Rightarrow \quad la_1 = 7 a_n = 3a_(n-1) \end{gathered}