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.

a_n=a_1r^(n-1)

SubstituteII

a_1= 13, r= - 3

a_n= 13( - 3)^(n-1)