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_n= r* a_(n-1); a_1= a_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 explicit rule, we can identify the common ratio r and the value of the first term a_1.
a_n= - 1/2( 1/4)^(n-1)
We can see that 14 is the common ratio and the first term is - 12. Now we have enough information to form a recursive rule for this sequence.
a_n=& 1/4a_(n-1);
a_1=& - 1/2
