Exercise 46 Page 448

The explicit rule of a geometric sequence combines the information provided by the two equations of the recursive rule 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 rules, r is the common ratio and a_1 is the first term. Looking at the given recursive rule, we can identify the common ratio r and the value of the first term a_1. a_1= - 4, a_n= 0.65a_(n-1) We can see that 0.65 is the common ratio and the first term is - 4. Now we have enough information to form an explicit rule for this sequence.

a_n=a_1r^(n-1)

SubstituteII

a_1= - 4, r= 0.65

a_n= - 4( 0.65)^(n-1)