Exercise 13 Page 316

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_n= r* a_(n-1); a_1= a_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= -2.5( 4)^(n-1) We can see that 4 is the common ratio and the first term is - 2.5. Now we have enough information to form an explicit formula for this sequence. \begin{gathered} a_n&={\color{#009600}{4}}a_{n-1}\\ a_1&={\color{#0000FF}{\text{-} 2.5}} \end{gathered}