5. Using Recursive Rules with Sequences
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Is it possible to find the common ratio and the first term just by looking at the explicit rule?
a_1=1/4, a_n=5a_(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= 1/4( 5)^(n-1) We can see that 5 is the common ratio and the first term is 14. Now we have enough information to form a recursive rule for this sequence. a_n=& 5a_(n-1); a_1=& 1/4