Exercise 25 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= 0.5a_(n-1); a_1= 16 We can see that 0.5 is the common ratio and the first term is 16. Now we have enough information to form an explicit formula for this sequence.