Exercise 11 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 recursive formula, we can identify the common ratio r and the value of the first term a_1. a_n= - 3 * a_(n-1); a_1= 13 We can see that - 3 is the common ratio and the first term is 13. Now we have enough information to form an explicit formula for this sequence. <deduct> a_n=a_1r^{n-1} a_1= 13, r= - 3 a_n={\color{#0000FF}{13}}({\color{#009600}{\text{-} 3}})^{n-1} </deduct>