Exercise 28 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_n= r* a_(n-1); & a_1= a_1 [0.8em] 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= - 5a_(n-1); a_1= 5 We can see that - 5 is the common ratio and the first term is 5. Now we have enough information to form an explicit formula for this sequence.

a_n=a_1(r)^(n-1)

SubstituteII

a_1= 5, r= - 5

a_n= 5( - 5)^(n-1)